Theorem reuimrmo

Description: Restricted uniqueness implies restricted "at most one" through implication, analogous to euimmo . (Contributed by Alexander van der Vekens, 25-Jun-2017)

	Ref	Expression
Assertion	reuimrmo	|- ( A. x e. A ( ph -> ps ) -> ( E! x e. A ps -> E* x e. A ph ) )

Proof

Step	Hyp	Ref	Expression
1		reurmo	|- ( E! x e. A ps -> E* x e. A ps )
2		rmoim	|- ( A. x e. A ( ph -> ps ) -> ( E* x e. A ps -> E* x e. A ph ) )
3	1 2	syl5	|- ( A. x e. A ( ph -> ps ) -> ( E! x e. A ps -> E* x e. A ph ) )