Theorem nornotOLD 1524

Description: Obsolete version of nornot 1523 as of 8-Dec-2023. (Contributed by Remi, 25-Oct-2023.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
nornotOLD	⊢ (¬ 𝜑 ↔ (𝜑 ⊽ 𝜑))

Proof of Theorem nornotOLD

Step	Hyp	Ref	Expression
1		pm4.56 985	. 2 ⊢ ((¬ 𝜑 ∧ ¬ 𝜑) ↔ ¬ (𝜑 ∨ 𝜑))
2		pm4.24 566	. 2 ⊢ (¬ 𝜑 ↔ (¬ 𝜑 ∧ ¬ 𝜑))
3		df-nor 1520	. 2 ⊢ ((𝜑 ⊽ 𝜑) ↔ ¬ (𝜑 ∨ 𝜑))
4	1, 2, 3	3bitr4i 305	1 ⊢ (¬ 𝜑 ↔ (𝜑 ⊽ 𝜑))

Syntax hints:  ¬ wn 3   ↔ wb 208   ∧ wa 398   ∨ wo 843   ⊽ wnor 1519

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 209  df-an 399  df-or 844  df-nor 1520

This theorem is referenced by: (None)