Theorem nfn 1548

Description: Inference associated with nfnt 1546. (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 1546	. 2 |- ( F/ x ph -> F/ x -. ph )
3	1, 2	ax-mp 7	1 |- F/ x -. ph

Syntax hints:   -. wn 3   F/wnf 1349

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ie2 1383  ax-4 1400  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350

This theorem is referenced by:  nfdc  1549  19.32dc  1569  nfnae  1610  mo2n  1928  nfne  2297  nfnel  2304  nfdif  3065  nfpo  4038  0neqopab  5550