Theorem bj-biexal3

Description: When ph is substituted for ps , both sides express a form of nonfreeness. (Contributed by BJ, 20-Oct-2019)

	Ref	Expression
Assertion	bj-biexal3	|- ( A. x ( ph -> A. x ps ) <-> A. x ( E. x ph -> ps ) )

Proof

Step	Hyp	Ref	Expression
1		bj-biexal1	|- ( A. x ( ph -> A. x ps ) <-> ( E. x ph -> A. x ps ) )
2		bj-biexal2	|- ( A. x ( E. x ph -> ps ) <-> ( E. x ph -> A. x ps ) )
3	1 2	bitr4i	|- ( A. x ( ph -> A. x ps ) <-> A. x ( E. x ph -> ps ) )