Theorem bj-nnfbii

Description: If two formulas are equivalent for all x , then nonfreeness of x in one of them is equivalent to nonfreeness in the other, inference form. See bj-nnfbi . (Contributed by BJ, 18-Nov-2023)

	Ref	Expression
Hypothesis	bj-nnfbii.1	|- ( ph <-> ps )
Assertion	bj-nnfbii	|- ( F// x ph <-> F// x ps )

Proof

Step	Hyp	Ref	Expression
1		bj-nnfbii.1	|- ( ph <-> ps )
2		bj-nnfbi	|- ( ( ( ph <-> ps ) /\ A. x ( ph <-> ps ) ) -> ( F// x ph <-> F// x ps ) )
3	1 2	bj-mpgs	|- ( F// x ph <-> F// x ps )