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	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
	ecase3d.2	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )
	ecase3d.3	⊢ ( 𝜑 → ( ¬ ( 𝜓 ∨ 𝜒 ) → 𝜃 ) )
Assertion	ecase3d	⊢ ( 𝜑 → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		ecase3d.1	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
2		ecase3d.2	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )
3		ecase3d.3	⊢ ( 𝜑 → ( ¬ ( 𝜓 ∨ 𝜒 ) → 𝜃 ) )
4	1 2	jaod	⊢ ( 𝜑 → ( ( 𝜓 ∨ 𝜒 ) → 𝜃 ) )
5	4 3	pm2.61d	⊢ ( 𝜑 → 𝜃 )