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Theorem exmoeu2 2326
Description: Existence implies "at most one" is equivalent to uniqueness. (Contributed by NM, 5-Apr-2004.)
Assertion
Ref Expression
exmoeu2  |-  ( E. x ph  ->  ( E* x ph  <->  E! x ph ) )

Proof of Theorem exmoeu2
StepHypRef Expression
1 eu5 2321 . 2  |-  ( E! x ph  <->  ( E. x ph  /\  E* x ph ) )
21baibr 874 1  |-  ( E. x ph  ->  ( E* x ph  <->  E! x ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178   E.wex 1551   E!weu 2283   E*wmo 2284
This theorem is referenced by:  fneu  5551
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288
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