Theorem nfnd 1769

Description: Deduction associated with nfnt 1767. (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 1767	. 2 ⊢ (Ⅎ𝑥𝜓 → Ⅎ𝑥 ¬ 𝜓)
3	1, 2	syl 17	1 ⊢ (𝜑 → Ⅎ𝑥 ¬ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4  Ⅎwnf 1699

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728

This theorem depends on definitions:  df-bi 196  df-or 384  df-ex 1696  df-nf 1701

This theorem is referenced by:  nfand  1814  hbnt  2129  nfexd  2153  cbvexd  2266  nfexd2  2320  nfned  2883  nfneld  2891  nfrexd  2989  axpowndlem3  9300  axpowndlem4  9301  axregndlem2  9304  axregnd  9305  distel  30953  bj-cbvexdv  31923