Theorem nfrd

Description: Consequence of the definition of not-free in a context. (Contributed by Wolf Lammen, 15-Oct-2021)

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

Proof

Step	Hyp	Ref	Expression
1		nfrd.1	|- ( ph -> F/ x ps )
2		df-nf	|- ( F/ x ps <-> ( E. x ps -> A. x ps ) )
3	1 2	sylib	|- ( ph -> ( E. x ps -> A. x ps ) )