Theorem exmo 2495

Description: Something exists or at most one exists. (Contributed by NM, 8-Mar-1995.)

Assertion

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

Proof of Theorem exmo

Step	Hyp	Ref	Expression
1		pm2.21 120	. . 3 |- ( -. E. x ph -> ( E. x ph -> E! x ph ) )
2		df-mo 2475	. . 3 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
3	1, 2	sylibr 224	. 2 |- ( -. E. x ph -> E* x ph )
4	3	orri 391	1 |- ( E. x ph \/ E* x ph )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 383   E.wex 1704   E!weu 2470   E*wmo 2471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385  df-mo 2475

This theorem is referenced by:  exmoeu  2502  moanim  2529  moexex  2541  mo2icl  3385  mosubopt  4972  dff3  6372  brdom3  9350  mof  32409