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Theorem euimmo 2080
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 2045 . 2  |-  ( E! x ps  ->  E* x ps )
2 moim 2077 . 2  |-  ( A. x ( ph  ->  ps )  ->  ( E* x ps  ->  E* x ph ) )
31, 2syl5 32 1  |-  ( A. x ( ph  ->  ps )  ->  ( E! x ps  ->  E* x ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1340   E!weu 2013   E*wmo 2014
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 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522
This theorem depends on definitions:  df-bi 116  df-nf 1448  df-sb 1750  df-eu 2016  df-mo 2017
This theorem is referenced by:  euim  2081  2eumo  2101  reuss2  3398
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