Theorem orim2d

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995)

	Ref	Expression
Hypothesis	orim1d.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	orim2d	⊢ ( 𝜑 → ( ( 𝜃 ∨ 𝜓 ) → ( 𝜃 ∨ 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		orim1d.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		idd	⊢ ( 𝜑 → ( 𝜃 → 𝜃 ) )
3	2 1	orim12d	⊢ ( 𝜑 → ( ( 𝜃 ∨ 𝜓 ) → ( 𝜃 ∨ 𝜒 ) ) )