Theorem nfn 1706

Description: Inference associated with nfnt 1704. (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 1704	. 2 ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)
3	1, 2	ax-mp 5	1 ⊢ Ⅎ𝑥 ¬ 𝜑

Syntax hints:  ¬ wn 3  Ⅎwnf 1509

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 619  ax-in2 620  ax-5 1496  ax-gen 1498  ax-ie2 1543  ax-4 1559  ax-ial 1583

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-fal 1404  df-nf 1510

This theorem is referenced by:  nfdc  1707  19.32dc  1727  nfnae  1770  mo2n  2107  nfne  2496  nfnel  2505  nfdif  3330  rabsnifsb  3741  nfpo  4404  0neqopab  6076  nfsup  7234  ismkvnex  7397  mkvprop  7400  zsupcllemstep  10535  oddpwdclemndvds  12806  ismkvnnlem  16768