Theorem nfnth 1728

Description: No variable is (effectively) free in a non-theorem. (Contributed by Mario Carneiro, 6-Dec-2016.) df-nf 1710 changed. (Revised by Wolf Lammen, 12-Sep-2021.)

Hypothesis

Ref	Expression
nfnth.1	|- -. ph

Assertion

Ref	Expression
nfnth	|- F/ x ph

Proof of Theorem nfnth

Step	Hyp	Ref	Expression
1		nfntht2 1720	. 2 |- ( A. x -. ph -> F/ x ph )
2		nfnth.1	. 2 |- -. ph
3	1, 2	mpg 1724	1 |- F/ x ph

Syntax hints:   -. wn 3   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722

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

This theorem is referenced by:  nffal  1732  nd1  9409  nd2  9410