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

Step	Hyp	Ref	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 ) )
3	1, 2	mprg 2378	1 |- ( E* x e. A ps -> E* x e. A ph )

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)