QUESTION: Let $O_1$, $O_2\subset \mathbb{R}^3$ be two open sets and $\phi:O_1\rightarrow O_2$ a diffeomorphism. If $S_1\subset O_1$ is a surface, then $S_2=\phi(S_1)$ is also a surface.
MY ATTEMPT: Due to $S_1$ be a surface then exists a parametrization $X: U\rightarrow S_1$ of $S_1$. Now, the hint is to show that $\phi\circ X: U\rightarrow S_2$ is a parametrization of $S_2$. But here is where I'm struggling. Would someone help me?