Theorem imor

Description: Implication in terms of disjunction. Theorem *4.6 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-1993)

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

Proof

Step	Hyp	Ref	Expression
1		notnotb	$$⊢\phi \leftrightarrow \neg \neg \phi$$
2	1	imbi1i	$$⊢\left(\phi \to \psi \right)\leftrightarrow \left(\neg \neg \phi \to \psi \right)$$
3		df-or	$$⊢\left(\neg \phi \vee \psi \right)\leftrightarrow \left(\neg \neg \phi \to \psi \right)$$
4	2 3	bitr4i	$$⊢\left(\phi \to \psi \right)\leftrightarrow \left(\neg \phi \vee \psi \right)$$