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Theorem rmoimia 2859
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 2858 . 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 2466 1  |-  ( E* x  e.  A  ps  ->  E* x  e.  A  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1465   E*wrmo 2396
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-eu 1980  df-mo 1981  df-ral 2398  df-rmo 2401
This theorem is referenced by: (None)
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