I think you're not comprehending some basic facts. Internet Explorer is a web browser, not a home page. Firefox is a web browser, not a home page. Likewise, Chrome, Opera, and Safari are web browsers, not home pages. Any website can be set as home page in any web browser. Yahoo.com is not a web browser; it is a website. You can set yahoo.com as your home page in whatever browser you're using.
If download and install Firefox, and set it as your default browser, then you could make yahoo.com your home page in Firefox. And, your email would go to your Yahoo! Mail Inbox, same as it does now when using Internet Explorer.
