Theorem pm5.61

Description: Theorem *5.61 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 30-Jun-2013)

	Ref	Expression
Assertion	pm5.61	$$⊢\left(\left(\phi \vee \psi \right)\wedge \neg \psi \right)\leftrightarrow \left(\phi \wedge \neg \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		orel2	$$⊢\neg \psi \to \left(\left(\phi \vee \psi \right)\to \phi \right)$$
2		orc	$$⊢\phi \to \left(\phi \vee \psi \right)$$
3	1 2	impbid1	$$⊢\neg \psi \to \left(\left(\phi \vee \psi \right)\leftrightarrow \phi \right)$$
4	3	pm5.32ri	$$⊢\left(\left(\phi \vee \psi \right)\wedge \neg \psi \right)\leftrightarrow \left(\phi \wedge \neg \psi \right)$$