Theorem nbbnOLD 386

Description: Obsolete version of nbbn 385 as of 10-Jun-2026. (Contributed by NM, 27-Jun-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
nbbnOLD	⊢ ((¬ 𝜑 ↔ 𝜓) ↔ ¬ (𝜑 ↔ 𝜓))

Proof of Theorem nbbnOLD

Step	Hyp	Ref	Expression
1		xor3 384	. 2 ⊢ (¬ (𝜑 ↔ 𝜓) ↔ (𝜑 ↔ ¬ 𝜓))
2		con2bi 355	. 2 ⊢ ((𝜑 ↔ ¬ 𝜓) ↔ (𝜓 ↔ ¬ 𝜑))
3		bicom 224	. 2 ⊢ ((𝜓 ↔ ¬ 𝜑) ↔ (¬ 𝜑 ↔ 𝜓))
4	1, 2, 3	3bitrri 300	1 ⊢ ((¬ 𝜑 ↔ 𝜓) ↔ ¬ (𝜑 ↔ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 208

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

This theorem is referenced by: (None)