How to prove that $a^x≡a \pmod N$

Question

I want to prove that $a^x≡a \pmod N$ where $x$ and $N$ are two positive integers, given that $x≡1 \pmod {\varphi(N)}$ and $\gcd(a,N)=1$. Problem is, if I prove these assuming $x$ and $N$ , where do I get value of $a$. I have only $x$ and $N$ , but i have to prove it with value of a. Kindly tell me how do I do it?