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	⊢ ( 𝜑 → 𝜒 )
	ecase3.2	⊢ ( 𝜓 → 𝜒 )
	ecase3.3	⊢ ( ¬ ( 𝜑 ∨ 𝜓 ) → 𝜒 )
Assertion	ecase3	⊢ 𝜒

Proof

Step	Hyp	Ref	Expression
1		ecase3.1	⊢ ( 𝜑 → 𝜒 )
2		ecase3.2	⊢ ( 𝜓 → 𝜒 )
3		ecase3.3	⊢ ( ¬ ( 𝜑 ∨ 𝜓 ) → 𝜒 )
4	1 2	jaoi	⊢ ( ( 𝜑 ∨ 𝜓 ) → 𝜒 )
5	4 3	pm2.61i	⊢ 𝜒