Theorem bj-nnfead

Description: Nonfreeness implies the equivalent of ax5ea , deduction form. (Contributed by BJ, 2-Dec-2023)

	Ref	Expression
Hypothesis	bj-nnfead.1	|- ( ph -> F// x ps )
Assertion	bj-nnfead	|- ( ph -> ( E. x ps -> A. x ps ) )

Proof

Step	Hyp	Ref	Expression
1		bj-nnfead.1	|- ( ph -> F// x ps )
2		bj-nnfea	|- ( F// x ps -> ( E. x ps -> A. x ps ) )
3	1 2	syl	|- ( ph -> ( E. x ps -> A. x ps ) )