Theorem nfnanOLD 2238

Description: Obsolete proof of nfnan 1830 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 1448	. 2 ⊢ ((𝜑 ⊼ 𝜓) ↔ ¬ (𝜑 ∧ 𝜓))
2		nfanOLDOLD.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3		nfanOLDOLD.2	. . . 4 ⊢ Ⅎ𝑥𝜓
4	2, 3	nfanOLDOLD 2237	. . 3 ⊢ Ⅎ𝑥(𝜑 ∧ 𝜓)
5	4	nfnOLD 2210	. 2 ⊢ Ⅎ𝑥 ¬ (𝜑 ∧ 𝜓)
6	1, 5	nfxfrOLD 1837	1 ⊢ Ⅎ𝑥(𝜑 ⊼ 𝜓)

Syntax hints:  ¬ wn 3   ∧ wa 384   ⊼ wnan 1447  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-nan 1448  df-ex 1705  df-nf 1710  df-nfOLD 1721

This theorem is referenced by: (None)