Theorem biorf

Description: A wff is equivalent to its disjunction with falsehood. Theorem *4.74 of WhiteheadRussell p. 121. (Contributed by NM, 23-Mar-1995) (Proof shortened by Wolf Lammen, 18-Nov-2012)

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

Proof

Step	Hyp	Ref	Expression
1		olc	$$⊢\psi \to \left(\phi \vee \psi \right)$$
2		orel1	$$⊢\neg \phi \to \left(\left(\phi \vee \psi \right)\to \psi \right)$$
3	1 2	impbid2	$$⊢\neg \phi \to \left(\psi \leftrightarrow \left(\phi \vee \psi \right)\right)$$