Metamath Proof Explorer


Theorem exmo

Description: Any proposition holds for some x or holds for at most one x . (Contributed by NM, 8-Mar-1995) Shorten proof and avoid df-eu . (Revised by BJ, 14-Oct-2022)

Ref Expression
Assertion exmo
|- ( E. x ph \/ E* x ph )

Proof

Step Hyp Ref Expression
1 nexmo
 |-  ( -. E. x ph -> E* x ph )
2 1 orri
 |-  ( E. x ph \/ E* x ph )