Theorem r19.21adva 1722

Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.)

Hypothesis

Ref	Expression
r19.21adva.1	|- ((ph /\ x e. A) -> (ps -> ch))

Assertion

Ref	Expression
r19.21adva	|- (ph -> (ps -> A.x e. A ch))

Distinct variable groups:   ph,x   ps,x

Proof of Theorem r19.21adva

Step	Hyp	Ref	Expression
1		r19.21adva.1	. . . 4 |- ((ph /\ x e. A) -> (ps -> ch))
2	1	ex 373	. . 3 |- (ph -> (x e. A -> (ps -> ch)))
3	2	com23 32	. 2 |- (ph -> (ps -> (x e. A -> ch)))
4	3	r19.21adv 1721	1 |- (ph -> (ps -> A.x e. A ch))

Syntax hints:   -> wi 3   /\ wa 223   e. wcel 960  A.wral 1648

This theorem is referenced by:  supxrunb1 6091  fsequb2 6525  faclbnd4lem4 6951  clsval2 7682  grpinveu 8060  0cnop 9898  0cnfn 9899

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980

This theorem depends on definitions:  df-bi 147  df-an 225  df-ral 1652

Copyright terms: Public domain