Theorem hbal 1436

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

Hypothesis

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

Assertion

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

Proof of Theorem hbal

Step	Hyp	Ref	Expression
1		hbal.1	. . 3 |- ( ph -> A. x ph )
2	1	alimi 1414	. 2 |- ( A. y ph -> A. y A. x ph )
3		ax-7 1407	. 2 |- ( A. y A. x ph -> A. x A. y ph )
4	2, 3	syl 14	1 |- ( A. y ph -> A. x A. y ph )

Syntax hints:   -> wi 4   A.wal 1312

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1406  ax-7 1407  ax-gen 1408

This theorem is referenced by:  hba2  1513  nfal  1538  aaanh  1548  hbex  1598  pm11.53  1849  euf  1980  hbral  2438