Theorem nfn 1706

Description: Inference associated with nfnt 1704. (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 1704	. 2 |- ( F/ x ph -> F/ x -. ph )
3	1, 2	ax-mp 5	1 |- F/ x -. ph

Syntax hints:   -. wn 3   F/wnf 1509

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 619  ax-in2 620  ax-5 1496  ax-gen 1498  ax-ie2 1543  ax-4 1559  ax-ial 1583

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-fal 1404  df-nf 1510

This theorem is referenced by:  nfdc  1707  19.32dc  1727  nfnae  1770  mo2n  2110  nfne  2507  nfnel  2516  nfdif  3344  rabsnifsb  3762  nfpo  4427  0neqopab  6106  nfsup  7296  ismkvnex  7459  mkvprop  7462  zsupcllemstep  10611  oddpwdclemndvds  12893  ismkvnnlem  16963