“if X then Y” means “(not X) or Y”

E.g. “If it’s raining, the sidewalk is wet.” That statement holds if it’s not raining or the sidewalk is wet.

This is a common occurrence in mathematics, where someone might not be able to unconditionally prove Y, but they can under the condition X. Later, another mathematician might build on this by proving X, thereby transitively proving Y. (Or conversely, they might unconditionally disprove Y, thereby disproving X.)

Many hard problems are answered this way.

For example, Fermat’s Last Theorem was proven assuming the Taniyama-Shimura-Weil Conjecture, then Wiles proved the conjecture.

Thousands of theorems rely on the the unproven Reinmann Hypothesis, which is why it’s so interesting to mathematicians.

But if your precondition is “stupid,” your proof is stupid.