Theorem nfri

Description: Consequence of the definition of not-free. (Contributed by Wolf Lammen, 16-Sep-2021)

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

Proof

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