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Theorem rmoimia 2978
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 2977 . 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 2625 1  |-  ( E* x  e.  A ps  ->  E* x  e.  A ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1696   E*wrmo 2559
This theorem is referenced by:  rmoimi  28057  2reu1  28067
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  df-ral 2561  df-rmo 2564
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