Theorem pm11.53v

Description: Version of pm11.53 with a disjoint variable condition, requiring fewer axioms. (Contributed by BJ, 7-Mar-2020)

	Ref	Expression
Assertion	pm11.53v	|- ( A. x A. y ( ph -> ps ) <-> ( E. x ph -> A. y ps ) )

Proof

Step	Hyp	Ref	Expression
1		19.21v	|- ( A. y ( ph -> ps ) <-> ( ph -> A. y ps ) )
2	1	albii	|- ( A. x A. y ( ph -> ps ) <-> A. x ( ph -> A. y ps ) )
3		19.23v	|- ( A. x ( ph -> A. y ps ) <-> ( E. x ph -> A. y ps ) )
4	2 3	bitri	|- ( A. x A. y ( ph -> ps ) <-> ( E. x ph -> A. y ps ) )