Theorem bj-nnfimd

Description: Nonfreeness in the antecedent and the consequent of an implication implies nonfreeness in the implication, deduction form. (Contributed by BJ, 2-Dec-2023)

	Ref	Expression
Hypotheses	bj-nnfimd.1	|- ( ph -> F// x ps )
	bj-nnfimd.2	|- ( ph -> F// x ch )
Assertion	bj-nnfimd	|- ( ph -> F// x ( ps -> ch ) )

Proof

Step	Hyp	Ref	Expression
1		bj-nnfimd.1	|- ( ph -> F// x ps )
2		bj-nnfimd.2	|- ( ph -> F// x ch )
3		bj-nnfim	|- ( ( F// x ps /\ F// x ch ) -> F// x ( ps -> ch ) )
4	1 2 3	syl2anc	|- ( ph -> F// x ( ps -> ch ) )