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Theorem euimmo 2205
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 2196 . 2  |-  ( E! x ps  ->  E* x ps )
2 moim 2202 . 2  |-  ( A. x ( ph  ->  ps )  ->  ( E* x ps  ->  E* x ph ) )
31, 2syl5 28 1  |-  ( A. x ( ph  ->  ps )  ->  ( E! x ps  ->  E* x ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   E!weu 2156   E*wmo 2157
This theorem is referenced by:  euim  2206  2eumo  2229  moeq3  2955  reuss2  3461
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161
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