1. The problem statement, all variables and given/known data Prove ∃x(P(x) → ∀y(P(y))). 2. Relevant equations 3. The attempt at a solution ∃x(P(x) → ∀y(P(y))) is equivalent to ∃x(¬P(x) ∨ ∀y(P(y))). This exercise is found in a section on "proofs involving disjunctions." I have tried many different ways to solve this and have a feeling I am not approaching it the right way. Perhaps I am not considering clever enough exhaustive cases? Can anyone direct me in the proper way to begin?