Theorem nf3andOLD 2233

Description: Obsolete proof of nf3and 1827 as of 6-Oct-2021. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 16-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfandOLD.1	⊢ (𝜑 → Ⅎ𝑥𝜓)
nfandOLD.2	⊢ (𝜑 → Ⅎ𝑥𝜒)
nfand.3OLD	⊢ (𝜑 → Ⅎ𝑥𝜃)

Assertion

Ref	Expression
nf3andOLD	⊢ (𝜑 → Ⅎ𝑥(𝜓 ∧ 𝜒 ∧ 𝜃))

Proof of Theorem nf3andOLD

Step	Hyp	Ref	Expression
1		df-3an 1039	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜓 ∧ 𝜒) ∧ 𝜃))
2		nfandOLD.1	. . . 4 ⊢ (𝜑 → Ⅎ𝑥𝜓)
3		nfandOLD.2	. . . 4 ⊢ (𝜑 → Ⅎ𝑥𝜒)
4	2, 3	nfandOLD 2232	. . 3 ⊢ (𝜑 → Ⅎ𝑥(𝜓 ∧ 𝜒))
5		nfand.3OLD	. . 3 ⊢ (𝜑 → Ⅎ𝑥𝜃)
6	4, 5	nfandOLD 2232	. 2 ⊢ (𝜑 → Ⅎ𝑥((𝜓 ∧ 𝜒) ∧ 𝜃))
7	1, 6	nfxfrdOLD 1838	1 ⊢ (𝜑 → Ⅎ𝑥(𝜓 ∧ 𝜒 ∧ 𝜃))

Syntax hints:   → wi 4   ∧ wa 384   ∧ w3a 1037  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-an 386  df-3an 1039  df-ex 1705  df-nf 1710  df-nfOLD 1721

This theorem is referenced by: (None)