Theorem nfndOLD 2199

Description: Obsolete proof of nfnd 1769 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nfndOLD.1	⊢ (𝜑 → Ⅎ𝑥𝜓)

Assertion

Ref	Expression
nfndOLD	⊢ (𝜑 → Ⅎ𝑥 ¬ 𝜓)

Proof of Theorem nfndOLD

Step	Hyp	Ref	Expression
1		nfndOLD.1	. 2 ⊢ (𝜑 → Ⅎ𝑥𝜓)
2		nfntOLD 2197	. 2 ⊢ (Ⅎ𝑥𝜓 → Ⅎ𝑥 ¬ 𝜓)
3	1, 2	syl 17	1 ⊢ (𝜑 → Ⅎ𝑥 ¬ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4  ℲwnfOLD 1700

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-or 384  df-ex 1696  df-nf 1701  df-nfOLD 1712

This theorem is referenced by:  nfandOLD  2220