Theorem r19.20ia 1697

Description: Inference quantifying both antecedent and consequent.

Hypothesis

Ref	Expression
r19.20ia.1	|- ((x e. A /\ ph) -> ps)

Assertion

Ref	Expression
r19.20ia	|- (A.x e. A ph -> A.x e. A ps)

Proof of Theorem r19.20ia

Step	Hyp	Ref	Expression
1		r19.20ia.1	. . 3 |- ((x e. A /\ ph) -> ps)
2	1	ex 373	. 2 |- (x e. A -> (ph -> ps))
3	2	r19.20i 1696	1 |- (A.x e. A ph -> A.x e. A ps)

Syntax hints:   -> wi 3   /\ wa 223   e. wcel 955  A.wral 1637

This theorem is referenced by:  tz7.48-2 3942  serzcmp0 6993  climsub 7066  bcthlem30 7962  riesz4 9911  dmdbr6at 10256

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-4 970  ax-5o 972

This theorem depends on definitions:  df-bi 147  df-an 225  df-ral 1641

Copyright terms: Public domain