Theorem nforOLD 2244

Description: Obsolete proof of nfor 1834 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 385	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
2		nfOLD.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	nfnOLD 2210	. . 3 ⊢ Ⅎ𝑥 ¬ 𝜑
4		nfOLD.2	. . 3 ⊢ Ⅎ𝑥𝜓
5	3, 4	nfimOLD 2229	. 2 ⊢ Ⅎ𝑥(¬ 𝜑 → 𝜓)
6	1, 5	nfxfrOLD 1837	1 ⊢ Ⅎ𝑥(𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 383  ℲwnfOLD 1709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710  df-nfOLD 1721

This theorem is referenced by:  nf3orOLD  2245