Theorem pm5.21

Description: Two propositions are equivalent if they are both false. Theorem *5.21 of WhiteheadRussell p. 124. (Contributed by NM, 21-May-1994)

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

Proof

Step	Hyp	Ref	Expression
1		pm5.21im	$$⊢\neg \phi \to \left(\neg \psi \to \left(\phi \leftrightarrow \psi \right)\right)$$
2	1	imp	$$⊢\left(\neg \phi \wedge \neg \psi \right)\to \left(\phi \leftrightarrow \psi \right)$$