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Theorem exmoeu2 2025
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 2024 . 2  |-  ( E! x ph  <->  ( E. x ph  /\  E* x ph ) )
21baibr 890 1  |-  ( E. x ph  ->  ( E* x ph  <->  E! x ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   E.wex 1453   E!weu 1977   E*wmo 1978
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-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-eu 1980  df-mo 1981
This theorem is referenced by:  n0mmoeu  3349  fneu  5197
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