Theorem jaod

Description: Deduction disjoining the antecedents of two implications. (Contributed by NM, 18-Aug-1994)

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

Proof

Step	Hyp	Ref	Expression
1		jaod.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		jaod.2	⊢ ( 𝜑 → ( 𝜃 → 𝜒 ) )
3	1	com12	⊢ ( 𝜓 → ( 𝜑 → 𝜒 ) )
4	2	com12	⊢ ( 𝜃 → ( 𝜑 → 𝜒 ) )
5	3 4	jaoi	⊢ ( ( 𝜓 ∨ 𝜃 ) → ( 𝜑 → 𝜒 ) )
6	5	com12	⊢ ( 𝜑 → ( ( 𝜓 ∨ 𝜃 ) → 𝜒 ) )