Theorem bj-biexal1

Description: A general FOL biconditional that generalizes 19.9ht among others. For this and the following theorems, see also 19.35 , 19.21 , 19.23 . When ph is substituted for ps , both sides express a form of nonfreeness. (Contributed by BJ, 20-Oct-2019)

	Ref	Expression
Assertion	bj-biexal1	|- ( A. x ( ph -> A. x ps ) <-> ( E. x ph -> A. x ps ) )

Proof

Step	Hyp	Ref	Expression
1		nfa1	|- F/ x A. x ps
2	1	19.23	|- ( A. x ( ph -> A. x ps ) <-> ( E. x ph -> A. x ps ) )