Theorem reximia

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 10-Feb-1997) (Proof shortened by Wolf Lammen, 31-Oct-2024)

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

Proof

Step	Hyp	Ref	Expression
1		reximia.1	|- ( x e. A -> ( ph -> ps ) )
2	1	imdistani	|- ( ( x e. A /\ ph ) -> ( x e. A /\ ps ) )
3	2	reximi2	|- ( E. x e. A ph -> E. x e. A ps )