Theorem ecase3d

Description: Deduction for elimination by cases. (Contributed by NM, 2-May-1996) (Proof shortened by Andrew Salmon, 7-May-2011)

	Ref	Expression
Hypotheses	ecase3d.1	$$⊢\phi \to \left(\psi \to \theta \right)$$
	ecase3d.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
	ecase3d.3	$$⊢\phi \to \left(\neg \left(\psi \vee \chi \right)\to \theta \right)$$
Assertion	ecase3d	$$⊢\phi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		ecase3d.1	$$⊢\phi \to \left(\psi \to \theta \right)$$
2		ecase3d.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
3		ecase3d.3	$$⊢\phi \to \left(\neg \left(\psi \vee \chi \right)\to \theta \right)$$
4	1 2	jaod	$$⊢\phi \to \left(\left(\psi \vee \chi \right)\to \theta \right)$$
5	4 3	pm2.61d	$$⊢\phi \to \theta$$