Theorem ecase3

Description: Inference for elimination by cases. (Contributed by NM, 23-Mar-1995) (Proof shortened by Wolf Lammen, 26-Nov-2012)

	Ref	Expression
Hypotheses	ecase3.1	$$⊢\phi \to \chi$$
	ecase3.2	$$⊢\psi \to \chi$$
	ecase3.3	$$⊢\neg \left(\phi \vee \psi \right)\to \chi$$
Assertion	ecase3	$$⊢\chi$$

Proof

Step	Hyp	Ref	Expression
1		ecase3.1	$$⊢\phi \to \chi$$
2		ecase3.2	$$⊢\psi \to \chi$$
3		ecase3.3	$$⊢\neg \left(\phi \vee \psi \right)\to \chi$$
4	1 2	jaoi	$$⊢\left(\phi \vee \psi \right)\to \chi$$
5	4 3	pm2.61i	$$⊢\chi$$