Theorem nbbnOLD

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

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

Proof

Step	Hyp	Ref	Expression
1		xor3	⊢ ( ¬ ( 𝜑 ↔ 𝜓 ) ↔ ( 𝜑 ↔ ¬ 𝜓 ) )
2		con2bi	⊢ ( ( 𝜑 ↔ ¬ 𝜓 ) ↔ ( 𝜓 ↔ ¬ 𝜑 ) )
3		bicom	⊢ ( ( 𝜓 ↔ ¬ 𝜑 ) ↔ ( ¬ 𝜑 ↔ 𝜓 ) )
4	1 2 3	3bitrri	⊢ ( ( ¬ 𝜑 ↔ 𝜓 ) ↔ ¬ ( 𝜑 ↔ 𝜓 ) )