Theorem nfnd 1645

Description: Deduction associated with nfnt 1644. (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 1644	. 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 1448

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-5 1435  ax-gen 1437  ax-ie2 1482  ax-4 1498  ax-ial 1522

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-fal 1349  df-nf 1449

This theorem is referenced by:  nfned  2430  nfneld  2439  nfifd  3547