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Theorem rmoimia 2741
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 2740 . 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 2378 1  |-  ( E* x  e.  A  ps  ->  E* x  e.  A  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1393   E*wrmo 2309
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-ral 2311  df-rmo 2314
This theorem is referenced by: (None)
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