Theorem pm5.62

Description: Theorem *5.62 of WhiteheadRussell p. 125. (Contributed by Roy F. Longton, 21-Jun-2005)

	Ref	Expression
Assertion	pm5.62	$$⊢\left(\left(\phi \wedge \psi \right)\vee \neg \psi \right)\leftrightarrow \left(\phi \vee \neg \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		exmid	$$⊢\left(\psi \vee \neg \psi \right)$$
2		ordir	$$⊢\left(\left(\phi \wedge \psi \right)\vee \neg \psi \right)\leftrightarrow \left(\left(\phi \vee \neg \psi \right)\wedge \left(\psi \vee \neg \psi \right)\right)$$
3	1 2	mpbiran2	$$⊢\left(\left(\phi \wedge \psi \right)\vee \neg \psi \right)\leftrightarrow \left(\phi \vee \neg \psi \right)$$