Theorem mpjaodan

Description: Eliminate a disjunction in a deduction. A translation of natural deduction rule \/ E ( \/ elimination), see natded . (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypotheses	jaodan.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
	jaodan.2	$$⊢\left(\phi \wedge \theta \right)\to \chi$$
	jaodan.3	$$⊢\phi \to \left(\psi \vee \theta \right)$$
Assertion	mpjaodan	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		jaodan.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
2		jaodan.2	$$⊢\left(\phi \wedge \theta \right)\to \chi$$
3		jaodan.3	$$⊢\phi \to \left(\psi \vee \theta \right)$$
4	1 2	jaodan	$$⊢\left(\phi \wedge \left(\psi \vee \theta \right)\right)\to \chi$$
5	3 4	mpdan	$$⊢\phi \to \chi$$