Theorem cdeqal

Description: Distribute conditional equality over quantification. (Contributed by Mario Carneiro, 11-Aug-2016)

	Ref	Expression
Hypothesis	cdeqnot.1	|- CondEq ( x = y -> ( ph <-> ps ) )
Assertion	cdeqal	|- CondEq ( x = y -> ( A. z ph <-> A. z ps ) )

Proof

Step	Hyp	Ref	Expression
1		cdeqnot.1	|- CondEq ( x = y -> ( ph <-> ps ) )
2	1	cdeqri	|- ( x = y -> ( ph <-> ps ) )
3	2	albidv	|- ( x = y -> ( A. z ph <-> A. z ps ) )
4	3	cdeqi	|- CondEq ( x = y -> ( A. z ph <-> A. z ps ) )