Filed by AmSurg Corp.

Pursuant to Rule 425 under the Securities Act of 1933, as amended

and deemed filed pursuant to Rule 14a-12

under the Securities Exchange Act of 1934, as amended

Subject Company: Envision Healthcare Holdings, Inc.

Commission File No. 001-36048

Dear Sheridan Clinicians,

Yesterday you received a letter from AMSURG CEO Chris Holden and Envision Healthcare CEO Bill Sanger announcing our plans to merge and form a compelling new healthcare services company - a leading and comprehensive national provider of outsourced clinical services, with complementary positions in medical transportation, ambulatory surgery and population health management.

I encourage you all to read these materials, as well as our joint press release. We believe AMSURG | Sheridan and Envision are highly complementary, both strategically and financially. We have proposed a true partnership that creates exciting new growth opportunities, and positions us to be an industry leader in physician services as the trend toward more comprehensive strategic relationships with health systems intensifies. The healthcare industry is dynamic and currently in a period of consolidation. We believe it is important to stay strategically proactive – to lead the transformation and control our own destiny. And we see this as extending our commitment to becoming the preferred “home” for physicians across multiple service lines – a place where you have a strong voice in a changing healthcare landscape.

Here are a few key points I would like you to keep in mind as you digest the news, and to assist in your communication with hospital clients:

• At this point, we have signed a merger agreement, but there is still significant work to be done, and likely several months of time, required before closing. In the meantime, it will be business as usual with no impact on clinical operations.

• Sheridan’s senior leadership, including Dr. Gilbert Drozdow and myself, have been intimately involved in this process and remain committed to this organization and its successful future in combination with Envision.

• When we do come together, it should have minimal impact on our clinical operations, and only enhance our ability to deliver resources and tools to our physicians and hospital clients. Most of the physician services specialties are complementary, as opposed to overlapping, across the two companies. In those few areas of overlap, we will work quickly and transparently with specialty leadership to develop an integration plan. We believe the experience we gained through the smooth integration of AMSURG and Sheridan will give us a distinct advantage.

• As with the AMSURG | Sheridan merger in 2014, we believe that Envision shares many key aspects of our culture, including a commitment to improving quality of care and a desire to support physicians and help them adapt to change. In developing our strategy and our joint communications surrounding this merger, it was very easy to agree to the phrase “provider led” as a key component.

• The combined company will be based in both Nashville, Tennessee and Greenwood Village, Colorado (Envision’s current corporate headquarters), and we will maintain our presence in Sunrise, FL. We do not expect to alter our regional support in any significant way.

• References to synergies include revenue opportunities, and on the cost side relate mostly to efficiencies gained through consolidation of our third party vendor relationships and operational scale we gain in overlapping markets. They do not correspond to changing our staffing models, compensation or benefit plans.

As always, thank you for your continued hard work and commitment. Without it, we would not be in a position to take this important strategic step forward.

Sincerely,

Robert Coward

President, Sheridan Healthcare

No Offer or Solicitation / Additional Information and Where to Find It

This communication is for informational purposes only and does not constitute an offer to sell or the solicitation of an offer to buy any securities or a solicitation of any vote or approval with respect to the proposed business combination between Envision and AMSURG or otherwise, nor shall there be any sale, issuance or transfer of securities in any jurisdiction in contravention of applicable law. No offer of securities shall be made except by means of a prospectus meeting the requirements of Section 10 of the Securities Act of 1933, as amended. The proposed business combination between Envision and AMSURG will be submitted to their respective shareholders for consideration. AMSURG will cause its newly formed, wholly owned subsidiary (“Newco”), to file with the Securities and Exchange Commission (the “SEC”) a Registration Statement on Form S-4 that will constitute a prospectus of Newco and a joint proxy statement of Envision and AMSURG. Envision and AMSURG will deliver the joint proxy statement/prospectus to their respective shareholders as required by applicable law. This communication is not a substitute for any prospectus, proxy statement or any other document that may be filed with the SEC in connection with the proposed business combination. INVESTORS AND SHAREHOLDERS ARE URGED TO READ THE JOINT PROXY STATEMENT/PROSPECTUS AND ANY OTHER RELEVANT DOCUMENTS THAT WILL BE FILED WITH THE SEC CAREFULLY AND IN THEIR ENTIRETY WHEN THEY BECOME AVAILABLE BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION ABOUT THE PROPOSED BUSINESS COMBINATION AND RELATED MATTERS. Investors and shareholders will be able to obtain free copies of the joint proxy statement/prospectus and other documents containing important information about Envision, AMSURG and Newco, once such documents are filed with the SEC, through the website maintained by the SEC at www.sec.gov. Envision and AMSURG make available free of charge at www.evhc.net and www. AMSURG.com, respectively (in the “Investors” section), copies of materials they file with, or furnish to, the SEC.

Participants in the Merger Solicitation

Envision, AMSURG and certain of their respective directors, executive officers and other members of management and employees may be deemed to be participants in the solicitation of proxies from the shareholders of Envision and AMSURG in connection with the proposed business combination. Information

about the directors and executive officers of Envision is set forth in its proxy statement for its 2016 annual meeting of shareholders filed with the SEC on March 23, 2016. Information about the directors and executive officers of AMSURG is set forth in its proxy statement for its 2016 annual meeting of shareholders filed with the SEC on April 22, 2016 and its Annual Report on Form 10-K for the year ended December 31, 2015 filed with the SEC on February 25, 2016. These documents can be obtained free of charge from the sources indicated above. Other information regarding those persons who are, under the rules of the SEC, participants in the proxy solicitation and a description of their direct and indirect interests, by security holdings or otherwise, will be contained in the joint proxy statement/prospectus and other relevant materials to be filed with the SEC when they become available.

Forward-Looking Statements

Certain statements and information in this presentation may be deemed to be “forward-looking statements” within the meaning of the Federal Private Securities Litigation Reform Act of 1995. Forward-looking statements may include, but are not limited to, statements relating to Envision’s and AMSURG’s objectives, plans and strategies, and all statements (other than statements of historical facts) that address activities, events or developments that Envision and AMSURG intend, expect, project, believe or anticipate will or may occur in the future. These statements are often characterized by terminology such as “believe,” “hope,” “may,” “anticipate,” “should,” “intend,” “plan,” “will,” “expect,” “estimate,” “project,” “positioned,” “strategy” and similar expressions, and are based on assumptions and assessments made by Envision’s and AMSURG’s management in light of their experience and their perception of historical trends, current conditions, expected future developments, and other factors they believe to be appropriate. Any forward-looking statements in this presentation are made as of the date hereof, and Envision and AMSURG undertake no duty to update or revise any such statements, whether as a result of new information, future events or otherwise. Forward-looking statements are not guarantees of future performance. Whether actual results will conform to expectations and predictions is subject to known and unknown risks and uncertainties, including: (i) risks and uncertainties discussed in the reports that Envision and AMSURG have filed with the SEC; (ii) general economic, market, or business conditions; (iii) risks associated with the ability to consummate the business combination between Envision and AMSURG and the timing of the closing of the business combination; (iv) the ability to successfully integrate Envision’s and AMSURG’s operations and employees; (v) the ability to realize anticipated benefits and synergies of the business combination; (vi) the potential impact of announcement of the business combination or consummation of the transaction on relationships, including with employees, customers and competitors; and (vii) other circumstances beyond Envision’s and AMSURG’s control. Refer to the section entitled “Risk Factors” in Envision’s and AMSURG’s annual and quarterly reports for a discussion of important factors that could cause actual results, developments and business decisions to differ materially from forward-looking statements.