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Theorem exmoeu2 2086
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 2085 . 2  |-  ( E! x ph  <->  ( E. x ph  /\  E* x ph ) )
21baibr 921 1  |-  ( E. x ph  ->  ( E* x ph  <->  E! x ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 105   E.wex 1503   E!weu 2038   E*wmo 2039
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-eu 2041  df-mo 2042
This theorem is referenced by:  n0mmoeu  3454  fneu  5339
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