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Theorem exmonim 2050
Description: There is at most one of something which does not exist. Unlike exmodc 2049 there is no decidability condition. (Contributed by Jim Kingdon, 22-Sep-2018.)
Assertion
Ref Expression
exmonim  |-  ( -. 
E. x ph  ->  E* x ph )

Proof of Theorem exmonim
StepHypRef Expression
1 pm2.21 606 . 2  |-  ( -. 
E. x ph  ->  ( E. x ph  ->  E! x ph ) )
2 df-mo 2003 . 2  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
31, 2sylibr 133 1  |-  ( -. 
E. x ph  ->  E* x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   E.wex 1468   E!weu 1999   E*wmo 2000
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 604
This theorem depends on definitions:  df-bi 116  df-mo 2003
This theorem is referenced by: (None)
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