Theorem nfn 1681

Description: Inference associated with nfnt 1679. (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 1679	. 2 |- ( F/ x ph -> F/ x -. ph )
3	1, 2	ax-mp 5	1 |- F/ x -. ph

Syntax hints:   -. wn 3   F/wnf 1483

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 1470  ax-gen 1472  ax-ie2 1517  ax-4 1533  ax-ial 1557

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-fal 1379  df-nf 1484

This theorem is referenced by:  nfdc  1682  19.32dc  1702  nfnae  1745  mo2n  2082  nfne  2469  nfnel  2478  nfdif  3294  nfpo  4348  0neqopab  5990  nfsup  7094  ismkvnex  7257  mkvprop  7260  zsupcllemstep  10372  oddpwdclemndvds  12493  ismkvnnlem  15995