I'm having difficulty with this proof since I'm not sure how the two iffs affect the layout of the solution:

Show that two simple graphs $\displaystyle G$ and $\displaystyle H$ are isomorphic if and only if there is a bijection $\displaystyle \vartheta : V(G) \rightarrow V(H)$ such that $\displaystyle uv \in E(G)$ if and only if $\displaystyle \vartheta (u) \vartheta (v) \in E(H)$.

Any help would be much appreciated,

Ultros