Theorem nfanOLD 1829

Description: Obsolete proof of nfan 1828 as of 9-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 13-Jan-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
nfan.1	⊢ Ⅎ𝑥𝜑
nfan.2	⊢ Ⅎ𝑥𝜓

Assertion

Ref	Expression
nfanOLD	⊢ Ⅎ𝑥(𝜑 ∧ 𝜓)

Proof of Theorem nfanOLD

Step	Hyp	Ref	Expression
1		df-an 386	. 2 ⊢ ((𝜑 ∧ 𝜓) ↔ ¬ (𝜑 → ¬ 𝜓))
2		nfan.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3		nfan.2	. . . . 5 ⊢ Ⅎ𝑥𝜓
4	3	nfn 1784	. . . 4 ⊢ Ⅎ𝑥 ¬ 𝜓
5	2, 4	nfim 1825	. . 3 ⊢ Ⅎ𝑥(𝜑 → ¬ 𝜓)
6	5	nfn 1784	. 2 ⊢ Ⅎ𝑥 ¬ (𝜑 → ¬ 𝜓)
7	1, 6	nfxfr 1779	1 ⊢ Ⅎ𝑥(𝜑 ∧ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 384  Ⅎwnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)