Theorem nfntOLD 2209

Description: Obsolete proof of nfnt 1782 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 28-Dec-2017.) (Revised by BJ, 24-Jul-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
nfntOLD	|- ( F/ x ph -> F/ x -. ph )

Proof of Theorem nfntOLD

Step	Hyp	Ref	Expression
1		nfnf1OLDOLD 2208	. 2 |- F/ x F/ x ph
2		df-nfOLD 1721	. . 3 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
3		hbnt 2144	. . 3 |- ( A. x ( ph -> A. x ph ) -> ( -. ph -> A. x -. ph ) )
4	2, 3	sylbi 207	. 2 |- ( F/ x ph -> ( -. ph -> A. x -. ph ) )
5	1, 4	nfdOLD 2193	1 |- ( F/ x ph -> F/ x -. ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481   F/wnfOLD 1709

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-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710  df-nfOLD 1721

This theorem is referenced by:  nfnOLD  2210  nfndOLD  2211  19.23tOLD  2218