Theorem hbald 1740

Description: Deduction form of bound-variable hypothesis builder hbal 1736. (Contributed by NM, 2-Jan-2002.)

Hypotheses

Ref	Expression
hbald.1	|- (ph -> A.yph)
hbald.2	|- (ph -> (ps -> A.xps))

Assertion

Ref	Expression
hbald	|- (ph -> (A.yps -> A.xA.yps))

Proof of Theorem hbald

Step	Hyp	Ref	Expression
1		hbald.1	. . 3 |- (ph -> A.yph)
2		hbald.2	. . 3 |- (ph -> (ps -> A.xps))
3	1, 2	alimdh 1563	. 2 |- (ph -> (A.yps -> A.yA.xps))
4		ax-7 1734	. 2 |- (A.yA.xps -> A.xA.yps)
5	3, 4	syl6 29	1 |- (ph -> (A.yps -> A.xA.yps))

Syntax hints:   -> wi 4  A.wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1546  ax-5 1557  ax-7 1734

This theorem is referenced by:  dvelimhw  1849  nfald  1852  dvelimv  1939  dvelimh  1964  dvelimALT  2133  dvelimf-o  2180