MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  exmo Unicode version

Theorem exmo 2283
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 pm2.21 102 . . 3  |-  ( -. 
E. x ph  ->  ( E. x ph  ->  E! x ph ) )
2 df-mo 2243 . . 3  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
31, 2sylibr 204 . 2  |-  ( -. 
E. x ph  ->  E* x ph )
43orri 366 1  |-  ( E. x ph  \/  E* x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 358   E.wex 1547   E!weu 2238   E*wmo 2239
This theorem is referenced by:  moexex  2307  mo2icl  3056  mosubopt  4395  dff3  5821  brdom3  8339  mof  25874
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-or 360  df-mo 2243
  Copyright terms: Public domain W3C validator