Theorem olcd

Description: Deduction introducing a disjunct. A translation of natural deduction rule \/ IL ( \/ insertion left), see natded . (Contributed by NM, 11-Apr-2008) (Proof shortened by Wolf Lammen, 3-Oct-2013)

	Ref	Expression
Hypothesis	orcd.1	$$⊢\phi \to \psi$$
Assertion	olcd	$$⊢\phi \to \left(\chi \vee \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		orcd.1	$$⊢\phi \to \psi$$
2	1	orcd	$$⊢\phi \to \left(\psi \vee \chi \right)$$
3	2	orcomd	$$⊢\phi \to \left(\chi \vee \psi \right)$$