Theorem nfnd 1587

Description: Deduction associated with nfnt 1586. (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 1586	. 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 1389

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-5 1376  ax-gen 1378  ax-ie2 1423  ax-4 1440  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290  df-nf 1390

This theorem is referenced by:  nfned  2338  nfneld  2347  nfifd  3376