Theorem nfi 1714

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

Hypothesis

Ref	Expression
nfi.1	|- ( E. x ph -> A. x ph )

Assertion

Ref	Expression
nfi	|- F/ x ph

Proof of Theorem nfi

Step	Hyp	Ref	Expression
1		nfi.1	. 2 |- ( E. x ph -> A. x ph )
2		df-nf 1710	. 2 |- ( F/ x ph <-> ( E. x ph -> A. x ph ) )
3	1, 2	mpbir 221	1 |- F/ x ph

Syntax hints:   -> wi 4   A.wal 1481   E.wex 1704   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-nf 1710

This theorem is referenced by:  nfv  1843