Theorem exmo 2293

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		pm2.21 111	. . 3 |- ( -. E. x ph -> ( E. x ph -> E! x ph ) )
2		df-mo 2271	. . 3 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
3	1, 2	sylibr 215	. 2 |- ( -. E. x ph -> E* x ph )
4	3	orri 377	1 |- ( E. x ph \/ E* x ph )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 369   E.wex 1659   E!weu 2266   E*wmo 2267

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 188  df-or 371  df-mo 2271

This theorem is referenced by:  exmoeu  2300  moanim  2328  moexex  2341  mo2icl  3256  mosubopt  4719  dff3  6050  brdom3  8954  mof  30855