Isomorphism from inner direct product to external how to prove the following:

Question

Let $$\phi_1:G_1 \to G_3$$ $$\phi_2:G_2 \to G_4$$ be isomophisms where $G_1 , G_2,G_3$ and $G_4$ are all groups.

How can I prove that $$\phi:G_1\oplus G_2 \to G_3 \oplus G_4 $$ is an isomorphism where $$\phi(x,y)=(\phi_1(x),\phi_2(y))$$ where $ x\in G_1, y \in G_2$.

Note that $(x,y) = (z,w)$.