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 849  df-ex 1780  df-nf 1784

This theorem is referenced by:  nfand  1897  nfan1  2200  hbnt  2294  nfexd  2329  cbvexdw  2341  cbvexd  2413  nfexd2  2451  nfned  3044  nfneld  3055  nfrexdw  3310  nfrexd  3373  cbvexeqsetf  3495  axpowndlem3  10639  axpowndlem4  10640  axregndlem2  10643  axregnd  10644  cbvex1v  35088  axnulg  35106  distel  35804  bj-cbvexdv  36801  bj-nfexd  37139  wl-issetft  37583