Theorem r19.21be 2716

Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 21-Nov-1994.)

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 2713	. . 3 |- ((ph /\ x e. A) -> ps)
3	2	expcom 424	. 2 |- (x e. A -> (ph -> ps))
4	3	rgen 2680	1 |- A.x e. A (ph -> ps)

Syntax hints:   -> wi 4   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  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-ral 2620

This theorem is referenced by: (None)