Theorem nfn 1680

Description: Inference associated with nfnt 1678. (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 1678	. 2 ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)
3	1, 2	ax-mp 5	1 ⊢ Ⅎ𝑥 ¬ 𝜑

Syntax hints:  ¬ wn 3  Ⅎwnf 1482

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 615  ax-in2 616  ax-5 1469  ax-gen 1471  ax-ie2 1516  ax-4 1532  ax-ial 1556

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-fal 1378  df-nf 1483

This theorem is referenced by:  nfdc  1681  19.32dc  1701  nfnae  1744  mo2n  2081  nfne  2468  nfnel  2477  nfdif  3293  nfpo  4346  0neqopab  5980  nfsup  7076  ismkvnex  7239  mkvprop  7242  zsupcllemstep  10353  oddpwdclemndvds  12412  ismkvnnlem  15855