Theorem nfn 1682

Description: Inference associated with nfnt 1680. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
nfn.1	|- F/ x ph

Assertion

Ref	Expression
nfn	|- F/ x -. ph

Proof of Theorem nfn

Step	Hyp	Ref	Expression
1		nfn.1	. 2 |- F/ x ph
2		nfnt 1680	. 2 |- ( F/ x ph -> F/ x -. ph )
3	1, 2	ax-mp 5	1 |- F/ x -. ph

Syntax hints:   -. wn 3   F/wnf 1484

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 1471  ax-gen 1473  ax-ie2 1518  ax-4 1534  ax-ial 1558

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-fal 1379  df-nf 1485

This theorem is referenced by:  nfdc  1683  19.32dc  1703  nfnae  1746  mo2n  2083  nfne  2471  nfnel  2480  nfdif  3302  nfpo  4366  0neqopab  6013  nfsup  7120  ismkvnex  7283  mkvprop  7286  zsupcllemstep  10409  oddpwdclemndvds  12608  ismkvnnlem  16193