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  3325  nfpo  4391  0neqopab  6048  nfsup  7155  ismkvnex  7318  mkvprop  7321  zsupcllemstep  10444  oddpwdclemndvds  12688  ismkvnnlem  16379