Theorem nfn 1588

Description: Inference associated with nfnt 1586. (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 1586	. 2 |- ( F/ x ph -> F/ x -. ph )
3	1, 2	ax-mp 7	1 |- F/ x -. ph

Syntax hints:   -. wn 3   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:  nfdc  1589  19.32dc  1609  nfnae  1650  mo2n  1969  nfne  2337  nfnel  2346  nfdif  3093  nfpo  4056  0neqopab  5570  nfsup  6405  zsupcllemstep  10341  oddpwdclemndvds  10549