Theorem hbal 1736

Description: If x is not free in ph, it is not free in A.yph. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
hbal.1	|- (ph -> A.xph)

Assertion

Ref	Expression
hbal	|- (A.yph -> A.xA.yph)

Proof of Theorem hbal

Step	Hyp	Ref	Expression
1		hbal.1	. . 3 |- (ph -> A.xph)
2	1	alimi 1559	. 2 |- (A.yph -> A.yA.xph)
3		ax-7 1734	. 2 |- (A.yA.xph -> A.xA.yph)
4	2, 3	syl 15	1 |- (A.yph -> A.xA.yph)

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:  hbex  1841  nfal  1842  hbral  2663