Theorem rmoimia 2954

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 2953	. 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 2547	1 |- ( E* x e. A ps -> E* x e. A ph )

Syntax hints:   -> wi 4   e. wcel 2160   E*wrmo 2471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-eu 2041  df-mo 2042  df-ral 2473  df-rmo 2476

This theorem is referenced by: (None)