Chomp and strategy stealing

In Chomp players take turns eating a square of a grid and everything above and to the right of it. The bottom-left square a1 is poisoned: whoever is forced to eat it loses. A striking argument shows the first player can always win, without naming a single move.

Suppose the second player had a winning reply to the first player biting only the top-right square. Then the first player could have bitten that very square to reach the same winning position instead. Since one of the two must be winning, it has to be the first player. This is strategy stealing: you prove a winner exists by argument, even when the explicit strategy stays unknown.