Theorem nfnd 1650

Description: Deduction associated with nfnt 1649. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypothesis

Ref	Expression
nfnd.1	⊢ (𝜑 → Ⅎ𝑥𝜓)

Assertion

Ref	Expression
nfnd	⊢ (𝜑 → Ⅎ𝑥 ¬ 𝜓)

Proof of Theorem nfnd

Step	Hyp	Ref	Expression
1		nfnd.1	. 2 ⊢ (𝜑 → Ⅎ𝑥𝜓)
2		nfnt 1649	. 2 ⊢ (Ⅎ𝑥𝜓 → Ⅎ𝑥 ¬ 𝜓)
3	1, 2	syl 14	1 ⊢ (𝜑 → Ⅎ𝑥 ¬ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4  Ⅎwnf 1453

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 609  ax-in2 610  ax-5 1440  ax-gen 1442  ax-ie2 1487  ax-4 1503  ax-ial 1527

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-fal 1354  df-nf 1454

This theorem is referenced by:  nfned  2434  nfneld  2443  nfifd  3553