Theorem orabs

Description: Absorption of redundant internal disjunct. Compare Theorem *4.45 of WhiteheadRussell p. 119. (Contributed by NM, 21-Jun-1993) (Proof shortened by Wolf Lammen, 28-Feb-2014)

	Ref	Expression
Assertion	orabs	$$⊢\phi \leftrightarrow \left(\left(\phi \vee \psi \right)\wedge \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		orc	$$⊢\phi \to \left(\phi \vee \psi \right)$$
2	1	pm4.71ri	$$⊢\phi \leftrightarrow \left(\left(\phi \vee \psi \right)\wedge \phi \right)$$