Theorem rmoimia 2928

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 2927	. 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 2523	1 |- ( E* x e. A ps -> E* x e. A ph )

Syntax hints:   -> wi 4   e. wcel 2136   E*wrmo 2447

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 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751  df-eu 2017  df-mo 2018  df-ral 2449  df-rmo 2452

This theorem is referenced by: (None)