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Theorem reuimrmo 27932
Description: Restricted uniqueness implies restricted "at most one" through implication, analogous to euimmo 2330. (Contributed by Alexander van der Vekens, 25-Jun-2017.)
Assertion
Ref Expression
reuimrmo  |-  ( A. x  e.  A  ( ph  ->  ps )  -> 
( E! x  e.  A  ps  ->  E* x  e.  A ph ) )

Proof of Theorem reuimrmo
StepHypRef Expression
1 reurmo 2923 . 2  |-  ( E! x  e.  A  ps  ->  E* x  e.  A ps )
2 rmoim 3133 . 2  |-  ( A. x  e.  A  ( ph  ->  ps )  -> 
( E* x  e.  A ps  ->  E* x  e.  A ph ) )
31, 2syl5 30 1  |-  ( A. x  e.  A  ( ph  ->  ps )  -> 
( E! x  e.  A  ps  ->  E* x  e.  A ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wral 2705   E!wreu 2707   E*wrmo 2708
This theorem is referenced by:  2reurmo  27936
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 2285  df-mo 2286  df-ral 2710  df-rex 2711  df-reu 2712  df-rmo 2713
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