Theorem biortn

Description: A wff is equivalent to its negated disjunction with falsehood. (Contributed by NM, 9-Jul-2012)

	Ref	Expression
Assertion	biortn	$$⊢\phi \to \left(\psi \leftrightarrow \left(\neg \phi \vee \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		notnot	$$⊢\phi \to \neg \neg \phi$$
2		biorf	$$⊢\neg \neg \phi \to \left(\psi \leftrightarrow \left(\neg \phi \vee \psi \right)\right)$$
3	1 2	syl	$$⊢\phi \to \left(\psi \leftrightarrow \left(\neg \phi \vee \psi \right)\right)$$