Theorem ralimia 2687

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 19-Jul-1996.)

Hypothesis

Ref	Expression
ralimia.1	|- (x e. A -> (ph -> ps))

Assertion

Ref	Expression
ralimia	|- (A.x e. A ph -> A.x e. A ps)

Proof of Theorem ralimia

Step	Hyp	Ref	Expression
1		ralimia.1	. . 3 |- (x e. A -> (ph -> ps))
2	1	a2i 12	. 2 |- ((x e. A -> ph) -> (x e. A -> ps))
3	2	ralimi2 2686	1 |- (A.x e. A ph -> A.x e. A ps)

Syntax hints:   -> wi 4   e. wcel 1710  A.wral 2614

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This theorem depends on definitions:  df-bi 177  df-ral 2619

This theorem is referenced by:  ralimiaa  2688  ralimi  2689  r19.12  2727  rr19.3v  2980  rr19.28v  2981  ffvresb  5431