Theorem nfnanOLD 2274

Description: Obsolete proof of nfnan 1870 as of 6-Oct-2021. (Contributed by Scott Fenton, 2-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
nfnanOLD	⊢ Ⅎ𝑥(𝜑 ⊼ 𝜓)

Proof of Theorem nfnanOLD

Step	Hyp	Ref	Expression
1		df-nan 1488	. 2 ⊢ ((𝜑 ⊼ 𝜓) ↔ ¬ (𝜑 ∧ 𝜓))
2		nfanOLDOLD.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3		nfanOLDOLD.2	. . . 4 ⊢ Ⅎ𝑥𝜓
4	2, 3	nfanOLDOLD 2273	. . 3 ⊢ Ⅎ𝑥(𝜑 ∧ 𝜓)
5	4	nfnOLD 2246	. 2 ⊢ Ⅎ𝑥 ¬ (𝜑 ∧ 𝜓)
6	1, 5	nfxfrOLD 1877	1 ⊢ Ⅎ𝑥(𝜑 ⊼ 𝜓)

Syntax hints:  ¬ wn 3   ∧ wa 383   ⊼ wnan 1487  ℲwnfOLD 1749

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-12 2087

This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-nan 1488  df-ex 1745  df-nf 1750  df-nfOLD 1761

This theorem is referenced by: (None)