Theorem rmoimia

Description: Restricted "at most one" is preserved through implication (note wff reversal). (Contributed by Alexander van der Vekens, 17-Jun-2017)

	Ref	Expression
Hypothesis	rmoimia.1	|- ( x e. A -> ( ph -> ps ) )
Assertion	rmoimia	|- ( E* x e. A ps -> E* x e. A ph )

Proof

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