Projection is Surjection

Theorem
For two non-empty sets $$S$$ and $$T$$, the first projection and second projection are both surjections.

Generalized Version
For all non-empty sets $$S_1, S_2, \ldots, S_j, \ldots, S_n$$, the $j$th projection $$pr_j$$ on $$\prod_{i=1}^n S_i$$ is a surjection.

Proof
but fairly obvious.