Theorem nforOLD 2232

Description: Obsolete proof of nfor 1822 as of 6-Oct-2021. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfOLD.1	⊢ Ⅎ𝑥𝜑
nfOLD.2	⊢ Ⅎ𝑥𝜓

Assertion

Ref	Expression
nforOLD	⊢ Ⅎ𝑥(𝜑 ∨ 𝜓)

Proof of Theorem nforOLD

Step	Hyp	Ref	Expression
1		df-or 384	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
2		nfOLD.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	nfnOLD 2198	. . 3 ⊢ Ⅎ𝑥 ¬ 𝜑
4		nfOLD.2	. . 3 ⊢ Ⅎ𝑥𝜓
5	3, 4	nfimOLD 2217	. 2 ⊢ Ⅎ𝑥(¬ 𝜑 → 𝜓)
6	1, 5	nfxfrOLD 1825	1 ⊢ Ⅎ𝑥(𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 382  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:  nf3orOLD  2233