Theorem nannotOLD 1568

Description: Obsolete proof of nannot 1567 as of 19-Oct-2022. (Contributed by Jeff Hoffman, 19-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
nannotOLD	⊢ (¬ 𝜓 ↔ (𝜓 ⊼ 𝜓))

Proof of Theorem nannotOLD

Step	Hyp	Ref	Expression
1		df-nan 1558	. . 3 ⊢ ((𝜓 ⊼ 𝜓) ↔ ¬ (𝜓 ∧ 𝜓))
2		anidm 560	. . 3 ⊢ ((𝜓 ∧ 𝜓) ↔ 𝜓)
3	1, 2	xchbinx 326	. 2 ⊢ ((𝜓 ⊼ 𝜓) ↔ ¬ 𝜓)
4	3	bicomi 216	1 ⊢ (¬ 𝜓 ↔ (𝜓 ⊼ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 198   ∧ wa 386   ⊼ wnan 1557

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

This theorem depends on definitions:  df-bi 199  df-an 387  df-nan 1558

This theorem is referenced by: (None)