Theorem sbalv

Description: Quantify with new variable inside substitution. (Contributed by NM, 18-Aug-1993)

	Ref	Expression
Hypothesis	sbalv.1	|- ( [ y / x ] ph <-> ps )
Assertion	sbalv	|- ( [ y / x ] A. z ph <-> A. z ps )

Proof

Step	Hyp	Ref	Expression
1		sbalv.1	|- ( [ y / x ] ph <-> ps )
2		sbal	|- ( [ y / x ] A. z ph <-> A. z [ y / x ] ph )
3	1	albii	|- ( A. z [ y / x ] ph <-> A. z ps )
4	2 3	bitri	|- ( [ y / x ] A. z ph <-> A. z ps )