Theorem nfn 1704

Description: Inference associated with nfnt 1702. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
nfn.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
nfn	⊢ Ⅎ𝑥 ¬ 𝜑

Proof of Theorem nfn

Step	Hyp	Ref	Expression
1		nfn.1	. 2 ⊢ Ⅎ𝑥𝜑
2		nfnt 1702	. 2 ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)
3	1, 2	ax-mp 5	1 ⊢ Ⅎ𝑥 ¬ 𝜑

Syntax hints:  ¬ wn 3  Ⅎwnf 1506

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 617  ax-in2 618  ax-5 1493  ax-gen 1495  ax-ie2 1540  ax-4 1556  ax-ial 1580

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-fal 1401  df-nf 1507

This theorem is referenced by:  nfdc  1705  19.32dc  1725  nfnae  1768  mo2n  2105  nfne  2493  nfnel  2502  nfdif  3326  rabsnifsb  3735  nfpo  4396  0neqopab  6061  nfsup  7182  ismkvnex  7345  mkvprop  7348  zsupcllemstep  10479  oddpwdclemndvds  12733  ismkvnnlem  16592