Theorem nfn 1636

Description: Inference associated with nfnt 1634. (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 1634	. 2 ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)
3	1, 2	ax-mp 5	1 ⊢ Ⅎ𝑥 ¬ 𝜑

Syntax hints:  ¬ wn 3  Ⅎwnf 1436

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-5 1423  ax-gen 1425  ax-ie2 1470  ax-4 1487  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437

This theorem is referenced by:  nfdc  1637  19.32dc  1657  nfnae  1700  mo2n  2027  nfne  2401  nfnel  2410  nfdif  3197  nfpo  4223  0neqopab  5816  nfsup  6879  ismkvnex  7029  mkvprop  7032  zsupcllemstep  11638  oddpwdclemndvds  11849