Theorem exmo 2304

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		pm2.21 108	. . 3 |- ( -. E. x ph -> ( E. x ph -> E! x ph ) )
2		df-mo 2280	. . 3 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
3	1, 2	sylibr 212	. 2 |- ( -. E. x ph -> E* x ph )
4	3	orri 376	1 |- ( E. x ph \/ E* x ph )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 368   E.wex 1596   E!weu 2275   E*wmo 2276

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 185  df-or 370  df-mo 2280

This theorem is referenced by:  exmoeu  2311  moanim  2352  moexex  2371  moexexOLD  2372  mo2icl  3282  mosubopt  4745  dff3  6034  brdom3  8906  mof  29480