Theorem notbicom

Description: Commutative law for the negation of a biconditional. (Contributed by Glauco Siliprandi, 15-Feb-2025)

	Ref	Expression
Hypothesis	notbicom.1	⊢ ¬ ( 𝜑 ↔ 𝜓 )
Assertion	notbicom	⊢ ¬ ( 𝜓 ↔ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		notbicom.1	⊢ ¬ ( 𝜑 ↔ 𝜓 )
2		bicom	⊢ ( ( 𝜓 ↔ 𝜑 ) ↔ ( 𝜑 ↔ 𝜓 ) )
3	1 2	mtbir	⊢ ¬ ( 𝜓 ↔ 𝜑 )