Theorem nfnd 1667

Description: Deduction associated with nfnt 1666. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypothesis

Ref	Expression
nfnd.1	|- ( ph -> F/ x ps )

Assertion

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

Proof of Theorem nfnd

Step	Hyp	Ref	Expression
1		nfnd.1	. 2 |- ( ph -> F/ x ps )
2		nfnt 1666	. 2 |- ( F/ x ps -> F/ x -. ps )
3	1, 2	syl 14	1 |- ( ph -> F/ x -. ps )

Syntax hints:   -. wn 3   -> wi 4   F/wnf 1470

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-5 1457  ax-gen 1459  ax-ie2 1504  ax-4 1520  ax-ial 1544

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-fal 1369  df-nf 1471

This theorem is referenced by:  nfned  2453  nfneld  2462  nfifd  3575