Theorem nfandOLD 2232

Description: Obsolete proof of nfand 1826 as of 6-Oct-2021. (Contributed by Mario Carneiro, 7-Oct-2016.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
nfandOLD.1	⊢ (𝜑 → Ⅎ𝑥𝜓)
nfandOLD.2	⊢ (𝜑 → Ⅎ𝑥𝜒)

Assertion

Ref	Expression
nfandOLD	⊢ (𝜑 → Ⅎ𝑥(𝜓 ∧ 𝜒))

Proof of Theorem nfandOLD

Step	Hyp	Ref	Expression
1		df-an 386	. 2 ⊢ ((𝜓 ∧ 𝜒) ↔ ¬ (𝜓 → ¬ 𝜒))
2		nfandOLD.1	. . . 4 ⊢ (𝜑 → Ⅎ𝑥𝜓)
3		nfandOLD.2	. . . . 5 ⊢ (𝜑 → Ⅎ𝑥𝜒)
4	3	nfndOLD 2211	. . . 4 ⊢ (𝜑 → Ⅎ𝑥 ¬ 𝜒)
5	2, 4	nfimdOLD 2226	. . 3 ⊢ (𝜑 → Ⅎ𝑥(𝜓 → ¬ 𝜒))
6	5	nfndOLD 2211	. 2 ⊢ (𝜑 → Ⅎ𝑥 ¬ (𝜓 → ¬ 𝜒))
7	1, 6	nfxfrdOLD 1838	1 ⊢ (𝜑 → Ⅎ𝑥(𝜓 ∧ 𝜒))

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 384  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-ex 1705  df-nf 1710  df-nfOLD 1721

This theorem is referenced by:  nf3andOLD  2233  nfbidOLD  2242