Theorem nf3anOLD 2227

Description: Obsolete proof of nf3an 1819 as of 6-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfanOLDOLD.1	⊢ Ⅎ𝑥𝜑
nfanOLDOLD.2	⊢ Ⅎ𝑥𝜓
nfanOLD.3	⊢ Ⅎ𝑥𝜒

Assertion

Ref	Expression
nf3anOLD	⊢ Ⅎ𝑥(𝜑 ∧ 𝜓 ∧ 𝜒)

Proof of Theorem nf3anOLD

Step	Hyp	Ref	Expression
1		df-3an 1033	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒))
2		nfanOLDOLD.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3		nfanOLDOLD.2	. . . 4 ⊢ Ⅎ𝑥𝜓
4	2, 3	nfanOLDOLD 2225	. . 3 ⊢ Ⅎ𝑥(𝜑 ∧ 𝜓)
5		nfanOLD.3	. . 3 ⊢ Ⅎ𝑥𝜒
6	4, 5	nfanOLDOLD 2225	. 2 ⊢ Ⅎ𝑥((𝜑 ∧ 𝜓) ∧ 𝜒)
7	1, 6	nfxfrOLD 1825	1 ⊢ Ⅎ𝑥(𝜑 ∧ 𝜓 ∧ 𝜒)

Syntax hints:   ∧ wa 383   ∧ w3a 1031  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-12 2034

This theorem depends on definitions:  df-bi 196  df-an 385  df-3an 1033  df-ex 1696  df-nfOLD 1712

This theorem is referenced by:  hb3anOLD  2229