Theorem nfi

Description: Deduce that x is not free in ph from the definition. (Contributed by Wolf Lammen, 15-Sep-2021)

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

Proof

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