Theorem bj-nnfbd

Description: If two formulas are equivalent, then nonfreeness of a variable in one of them is equivalent to nonfreeness in the other, deduction form. See bj-nnfbi . (Contributed by BJ, 27-Aug-2023)

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

Proof

Step	Hyp	Ref	Expression
1		bj-nnfbd.1	|- ( ph -> ( ps <-> ch ) )
2		ax-5	|- ( ph -> A. x ph )
3	1	bj-nnfbd0	|- ( ( ph /\ A. x ph ) -> ( F// x ps <-> F// x ch ) )
4	2 3	mpdan	|- ( ph -> ( F// x ps <-> F// x ch ) )