Be $f:[0,1]\longrightarrow[0,1]$ a continuous function, prove that exists $x\in[0,1]$ so that $f(x)=x$ . Be $f:[0,1]\longrightarrow[0,1]$ a continuous function, prove that exists $x\in[0,1]$ so that $f(x)=x$ .
I am studying mathematical analysis in functions of one variable, and looking through my notes I can't find any theorem or proposition to help me prove it.

Hint.
Consider the function 
$$g(x)=f(x)-x$$
and use the intermediate value theorem (this is possible because $f$ is continuous) to prove that there exists $x\in [0,1]$ such that $g(x)=0$.
