Theorem nf3orOLD 2386

Description: Obsolete proof of nf3or 1980 as of 6-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfOLD.1	⊢ Ⅎ𝑥𝜑
nfOLD.2	⊢ Ⅎ𝑥𝜓
nfOLD.3	⊢ Ⅎ𝑥𝜒

Assertion

Ref	Expression
nf3orOLD	⊢ Ⅎ𝑥(𝜑 ∨ 𝜓 ∨ 𝜒)

Proof of Theorem nf3orOLD

Step	Hyp	Ref	Expression
1		df-3or 1073	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒))
2		nfOLD.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3		nfOLD.2	. . . 4 ⊢ Ⅎ𝑥𝜓
4	2, 3	nforOLD 2385	. . 3 ⊢ Ⅎ𝑥(𝜑 ∨ 𝜓)
5		nfOLD.3	. . 3 ⊢ Ⅎ𝑥𝜒
6	4, 5	nforOLD 2385	. 2 ⊢ Ⅎ𝑥((𝜑 ∨ 𝜓) ∨ 𝜒)
7	1, 6	nfxfrOLD 1982	1 ⊢ Ⅎ𝑥(𝜑 ∨ 𝜓 ∨ 𝜒)

Syntax hints:   ∨ wo 382   ∨ w3o 1071  ℲwnfOLD 1854

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1867  ax-4 1882  ax-5 1984  ax-6 2050  ax-7 2086  ax-10 2164  ax-12 2192

This theorem depends on definitions:  df-bi 197  df-or 384  df-3or 1073  df-ex 1850  df-nf 1855  df-nfOLD 1866

This theorem is referenced by: (None)