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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
StepHypRef 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 ) )
31, 2sylibr 215 . 2  |-  ( -. 
E. x ph  ->  E* x ph )
43orri 377 1  |-  ( E. x ph  \/  E* x ph )
Colors of variables: wff setvar class
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
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