Theorem nfnf1 2031

Description: The setvar x is not free in F/ x ph. (Contributed by Mario Carneiro, 11-Aug-2016.) Remove dependency on ax-12 2047. (Revised by Wolf Lammen, 12-Oct-2021.)

Assertion

Ref	Expression
nfnf1	|- F/ x F/ x ph

Proof of Theorem nfnf1

Step	Hyp	Ref	Expression
1		df-nf 1710	. 2 |- ( F/ x ph <-> ( E. x ph -> A. x ph ) )
2		nfe1 2027	. . 3 |- F/ x E. x ph
3		nfa1 2028	. . 3 |- F/ x A. x ph
4	2, 3	nfim 1825	. 2 |- F/ x ( E. x ph -> A. x ph )
5	1, 4	nfxfr 1779	1 |- F/ x 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  ax-gen 1722  ax-4 1737  ax-10 2019

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by:  nfaldOLD  2166  nfeqf2  2297  nfsb4t  2389  nfnfc1  2767  sbcnestgf  3995  dfnfc2OLD  4455  bj-sbf4  32827  wl-equsal1t  33327  wl-sb6rft  33330  wl-sb8t  33333  wl-mo2tf  33353  wl-eutf  33355  wl-mo2t  33357  wl-mo3t  33358  wl-sb8eut  33359