Theorem pm5.21im

Description: Two propositions are equivalent if they are both false. Closed form of 2false . Equivalent to a biimpr -like version of the xor-connective. (Contributed by Wolf Lammen, 13-May-2013)

	Ref	Expression
Assertion	pm5.21im	$$⊢\neg \phi \to \left(\neg \psi \to \left(\phi \leftrightarrow \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		nbn2	$$⊢\neg \phi \to \left(\neg \psi \leftrightarrow \left(\phi \leftrightarrow \psi \right)\right)$$
2	1	biimpd	$$⊢\neg \phi \to \left(\neg \psi \to \left(\phi \leftrightarrow \psi \right)\right)$$