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Theorem exmo 2323
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 pm2.21 112 . . 3  |-  ( -. 
E. x ph  ->  ( E. x ph  ->  E! x ph ) )
2 df-mo 2303 . . 3  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
31, 2sylibr 216 . 2  |-  ( -. 
E. x ph  ->  E* x ph )
43orri 378 1  |-  ( E. x ph  \/  E* x ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 370   E.wex 1662   E!weu 2298   E*wmo 2299
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 189  df-or 372  df-mo 2303
This theorem is referenced by:  exmoeu  2330  moanim  2357  moexex  2369  mo2icl  3216  mosubopt  4698  dff3  6033  brdom3  8953  mof  31063
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