Theorem nfn 1594

Description: Inference associated with nfnt 1592. (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 1592	. 2 ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)
3	1, 2	ax-mp 7	1 ⊢ Ⅎ𝑥 ¬ 𝜑

Syntax hints:  ¬ wn 3  Ⅎwnf 1395

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 580  ax-in2 581  ax-5 1382  ax-gen 1384  ax-ie2 1429  ax-4 1446  ax-ial 1473

This theorem depends on definitions:  df-bi 116  df-tru 1293  df-fal 1296  df-nf 1396

This theorem is referenced by:  nfdc  1595  19.32dc  1615  nfnae  1658  mo2n  1977  nfne  2349  nfnel  2358  nfdif  3122  nfpo  4137  0neqopab  5708  nfsup  6741  zsupcllemstep  11280  oddpwdclemndvds  11488