Theorem r19.21be 1269

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	. . . . 5 |- (ph -> A.x e. A ps)
2	1	r19.21bi 1266	. . . 4 |- ((ph /\ x e. A) -> ps)
3	2	ancoms 334	. . 3 |- ((x e. A /\ ph) -> ps)
4	3	exp 291	. 2 |- (x e. A -> (ph -> ps))
5	4	rgen 1247	1 |- A.x e. A (ph -> ps)

Syntax hints:   -> wi 2   e. wcel 1092  A.wral 1201

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ral 1205

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