Theorem nfandOLD 2220

Description: Obsolete proof of nfand 1814 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 385	. 2 ⊢ ((𝜓 ∧ 𝜒) ↔ ¬ (𝜓 → ¬ 𝜒))
2		nfandOLD.1	. . . 4 ⊢ (𝜑 → Ⅎ𝑥𝜓)
3		nfandOLD.2	. . . . 5 ⊢ (𝜑 → Ⅎ𝑥𝜒)
4	3	nfndOLD 2199	. . . 4 ⊢ (𝜑 → Ⅎ𝑥 ¬ 𝜒)
5	2, 4	nfimdOLD 2214	. . 3 ⊢ (𝜑 → Ⅎ𝑥(𝜓 → ¬ 𝜒))
6	5	nfndOLD 2199	. 2 ⊢ (𝜑 → Ⅎ𝑥 ¬ (𝜓 → ¬ 𝜒))
7	1, 6	nfxfrdOLD 1826	1 ⊢ (𝜑 → Ⅎ𝑥(𝜓 ∧ 𝜒))

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 383  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-10 2006  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-ex 1696  df-nf 1701  df-nfOLD 1712

This theorem is referenced by:  nf3andOLD  2221  nfbidOLD  2230