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	$$⊢\left(\neg \phi \leftrightarrow \psi \right)\leftrightarrow \neg \left(\phi \leftrightarrow \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		xor3	$$⊢\neg \left(\phi \leftrightarrow \psi \right)\leftrightarrow \left(\phi \leftrightarrow \neg \psi \right)$$
2		con2bi	$$⊢\left(\phi \leftrightarrow \neg \psi \right)\leftrightarrow \left(\psi \leftrightarrow \neg \phi \right)$$
3		bicom	$$⊢\left(\psi \leftrightarrow \neg \phi \right)\leftrightarrow \left(\neg \phi \leftrightarrow \psi \right)$$
4	1 2 3	3bitrri	$$⊢\left(\neg \phi \leftrightarrow \psi \right)\leftrightarrow \neg \left(\phi \leftrightarrow \psi \right)$$