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Theorem euimmo 2329
Description: Uniqueness implies "at most one" through implication. (Contributed by NM, 22-Apr-1995.)
Assertion
Ref Expression
euimmo  |-  ( A. x ( ph  ->  ps )  ->  ( E! x ps  ->  E* x ph ) )

Proof of Theorem euimmo
StepHypRef Expression
1 eumo 2320 . 2  |-  ( E! x ps  ->  E* x ps )
2 moim 2326 . 2  |-  ( A. x ( ph  ->  ps )  ->  ( E* x ps  ->  E* x ph ) )
31, 2syl5 30 1  |-  ( A. x ( ph  ->  ps )  ->  ( E! x ps  ->  E* x ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549   E!weu 2280   E*wmo 2281
This theorem is referenced by:  euim  2330  2eumo  2353  moeq3  3103  reuss2  3613
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285
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