Theorem mpjaod

Description: Eliminate a disjunction in a deduction. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypotheses	jaod.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	jaod.2	⊢ ( 𝜑 → ( 𝜃 → 𝜒 ) )
	jaod.3	⊢ ( 𝜑 → ( 𝜓 ∨ 𝜃 ) )
Assertion	mpjaod	⊢ ( 𝜑 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		jaod.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		jaod.2	⊢ ( 𝜑 → ( 𝜃 → 𝜒 ) )
3		jaod.3	⊢ ( 𝜑 → ( 𝜓 ∨ 𝜃 ) )
4	1 2	jaod	⊢ ( 𝜑 → ( ( 𝜓 ∨ 𝜃 ) → 𝜒 ) )
5	3 4	mpd	⊢ ( 𝜑 → 𝜒 )