Theorem notbicom

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

	Ref	Expression
Hypothesis	notbicom.1	$$⊢\neg \left(\phi \leftrightarrow \psi \right)$$
Assertion	notbicom	$$⊢\neg \left(\psi \leftrightarrow \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		notbicom.1	$$⊢\neg \left(\phi \leftrightarrow \psi \right)$$
2		bicom	$$⊢\left(\psi \leftrightarrow \phi \right)\leftrightarrow \left(\phi \leftrightarrow \psi \right)$$
3	1 2	mtbir	$$⊢\neg \left(\psi \leftrightarrow \phi \right)$$