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  2200  hbnt  2294  nfexd  2329  cbvexdw  2340  cbvexd  2412  nfexd2  2450  nfned  3034  nfneld  3045  nfrexdw  3290  nfrexd  3352  cbvexeqsetf  3474  axpowndlem3  10611  axpowndlem4  10612  axregndlem2  10615  axregnd  10616  cbvex1v  35051  axnulg  35069  distel  35767  bj-cbvexdv  36764  bj-nfexd  37102  wl-issetft  37546