Theorem nfnd 1858

Description: Deduction associated with nfnt 1856. (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 1856	. 2 ⊢ (Ⅎ𝑥𝜓 → Ⅎ𝑥 ¬ 𝜓)
3	1, 2	syl 17	1 ⊢ (𝜑 → Ⅎ𝑥 ¬ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4  Ⅎwnf 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809

This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1780  df-nf 1784

This theorem is referenced by:  nfand  1897  nfan1  2201  hbnt  2294  nfexd  2328  cbvexdw  2337  cbvexd  2407  nfexd2  2445  nfned  3028  nfneld  3039  nfrexdw  3286  nfrexd  3349  cbvexeqsetf  3465  axpowndlem3  10559  axpowndlem4  10560  axregndlem2  10563  axregnd  10564  cbvex1v  35071  axnulg  35089  distel  35798  bj-cbvexdv  36795  bj-nfexd  37133  wl-issetft  37577