Theorem orfa2

Description: Remove a contradicting disjunct from an antecedent. (Contributed by Giovanni Mascellani, 15-Sep-2017)

	Ref	Expression
Hypothesis	orfa2.1	$$⊢\phi \to \perp$$
Assertion	orfa2	$$⊢\left(\phi \vee \psi \right)\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		orfa2.1	$$⊢\phi \to \perp$$
2	1	orim1i	$$⊢\left(\phi \vee \psi \right)\to \left(\perp \vee \psi \right)$$
3		falim	$$⊢\perp \to \psi$$
4		id	$$⊢\psi \to \psi$$
5	3 4	jaoi	$$⊢\left(\perp \vee \psi \right)\to \psi$$
6	2 5	syl	$$⊢\left(\phi \vee \psi \right)\to \psi$$