Theorem ecase

Description: Inference for elimination by cases. (Contributed by NM, 13-Jul-2005)

	Ref	Expression
Hypotheses	ecase.1	⊢ ( ¬ 𝜑 → 𝜒 )
	ecase.2	⊢ ( ¬ 𝜓 → 𝜒 )
	ecase.3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
Assertion	ecase	⊢ 𝜒

Proof

Step	Hyp	Ref	Expression
1		ecase.1	⊢ ( ¬ 𝜑 → 𝜒 )
2		ecase.2	⊢ ( ¬ 𝜓 → 𝜒 )
3		ecase.3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
4	3	ex	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
5	4 1 2	pm2.61nii	⊢ 𝜒