Theorem mpjaod

Description: Eliminate a disjunction in a deduction. (Contributed by Mario Carneiro, 29-May-2016)

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

Proof

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