Theorem hbald 1471

Description: Deduction form of bound-variable hypothesis builder hbal 1457. (Contributed by NM, 2-Jan-2002.)

Hypotheses

Ref	Expression
hbald.1	|- ( ph -> A. y ph )
hbald.2	|- ( ph -> ( ps -> A. x ps ) )

Assertion

Ref	Expression
hbald	|- ( ph -> ( A. y ps -> A. x A. y ps ) )

Proof of Theorem hbald

Step	Hyp	Ref	Expression
1		hbald.1	. . 3 |- ( ph -> A. y ph )
2		hbald.2	. . 3 |- ( ph -> ( ps -> A. x ps ) )
3	1, 2	alimdh 1447	. 2 |- ( ph -> ( A. y ps -> A. y A. x ps ) )
4		ax-7 1428	. 2 |- ( A. y A. x ps -> A. x A. y ps )
5	3, 4	syl6 33	1 |- ( ph -> ( A. y ps -> A. x A. y ps ) )

Syntax hints:   -> wi 4   A.wal 1333

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1427  ax-7 1428  ax-gen 1429

This theorem is referenced by:  nfald  1740  dvelimfALT2  1797