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Theorem rmoimia 3134
Description: Restricted "at most one" is preserved through implication (note wff reversal). (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Hypothesis
Ref Expression
rmoimia.1  |-  ( x  e.  A  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
rmoimia  |-  ( E* x  e.  A ps  ->  E* x  e.  A ph )

Proof of Theorem rmoimia
StepHypRef Expression
1 rmoim 3133 . 2  |-  ( A. x  e.  A  ( ph  ->  ps )  -> 
( E* x  e.  A ps  ->  E* x  e.  A ph ) )
2 rmoimia.1 . 2  |-  ( x  e.  A  ->  ( ph  ->  ps ) )
31, 2mprg 2775 1  |-  ( E* x  e.  A ps  ->  E* x  e.  A ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   E*wrmo 2708
This theorem is referenced by:  rmoimi  27930  2reu1  27940
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-rmo 2713
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