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Theorem euimmo 2289
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 2280 . 2  |-  ( E! x ps  ->  E* x ps )
2 moim 2286 . 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 1546   E!weu 2240   E*wmo 2241
This theorem is referenced by:  euim  2290  2eumo  2313  moeq3  3056  reuss2  3566
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2244  df-mo 2245
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