Theorem r19.21be 1731

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

Hypothesis

Ref	Expression
r19.21be.1	|- (ph -> A.x e. A ps)

Assertion

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

Proof of Theorem r19.21be

Step	Hyp	Ref	Expression
1		r19.21be.1	. . . 4 |- (ph -> A.x e. A ps)
2	1	r19.21bi 1728	. . 3 |- ((ph /\ x e. A) -> ps)
3	2	expcom 374	. 2 |- (x e. A -> (ph -> ps))
4	3	rgen 1701	1 |- A.x e. A (ph -> ps)

Syntax hints:   -> wi 3   e. wcel 960  A.wral 1648

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

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

Copyright terms: Public domain