As you can see in "statement of the theorem" in http://en.wikipedia.org/wiki/Implicit_function_theorem" , or

perhaps a little clearer in Implicit Function Theorem -- from Wolfram MathWorld ,

this isthe exact wording of the implicit function theorem, so I don't understand what is italmost

that you cannot understand here?

Perhaps it is just a matter of writing so that it'll look clearer...?

Tonio