Theorem nfn 1669

Description: Inference associated with nfnt 1667. (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 1667	. 2 |- ( F/ x ph -> F/ x -. ph )
3	1, 2	ax-mp 5	1 |- F/ x -. ph

Syntax hints:   -. wn 3   F/wnf 1471

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 1458  ax-gen 1460  ax-ie2 1505  ax-4 1521  ax-ial 1545

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370  df-nf 1472

This theorem is referenced by:  nfdc  1670  19.32dc  1690  nfnae  1733  mo2n  2070  nfne  2457  nfnel  2466  nfdif  3280  nfpo  4332  0neqopab  5963  nfsup  7051  ismkvnex  7214  mkvprop  7217  zsupcllemstep  12082  oddpwdclemndvds  12309  ismkvnnlem  15542