Theorem ralimiaa 2689

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 4-Aug-2007.)

Hypothesis

Ref	Expression
ralimiaa.1	|- ((x e. A /\ ph) -> ps)

Assertion

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

Proof of Theorem ralimiaa

Step	Hyp	Ref	Expression
1		ralimiaa.1	. . 3 |- ((x e. A /\ ph) -> ps)
2	1	ex 423	. 2 |- (x e. A -> (ph -> ps))
3	2	ralimia 2688	1 |- (A.x e. A ph -> A.x e. A ps)

Syntax hints:   -> wi 4   /\ wa 358   e. wcel 1710  A.wral 2615

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-an 360  df-ral 2620

This theorem is referenced by: (None)