Theorem bj-nnf-cbvaliv

Description: The only DV conditions are those saying that y is a fresh variable used to construct ch . (Contributed by BJ, 4-Apr-2026)

	Ref	Expression
Hypotheses	bj-nnf-cbvaliv.nf0	|- ( ph -> A. x ph )
	bj-nnf-cbvaliv.nf	|- ( ph -> F// x ch )
	bj-nnf-cbvaliv.is	|- ( ( ph /\ x = y ) -> ( ps -> ch ) )
Assertion	bj-nnf-cbvaliv	|- ( ph -> ( A. x ps -> A. y ch ) )

Proof

Step	Hyp	Ref	Expression
1		bj-nnf-cbvaliv.nf0	|- ( ph -> A. x ph )
2		bj-nnf-cbvaliv.nf	|- ( ph -> F// x ch )
3		bj-nnf-cbvaliv.is	|- ( ( ph /\ x = y ) -> ( ps -> ch ) )
4		ax-5	|- ( ph -> A. y ph )
5		ax-5	|- ( A. x ps -> A. y A. x ps )
6	1 2 3	bj-nnf-spim	|- ( ph -> ( A. x ps -> ch ) )
7	4 5 6	alrimdh	|- ( ph -> ( A. x ps -> A. y ch ) )