Theorem jao1i

Description: Add a disjunct in the antecedent of an implication. (Contributed by Rodolfo Medina, 24-Sep-2010)

	Ref	Expression
Hypothesis	jao1i.1	$$⊢\psi \to \left(\chi \to \phi \right)$$
Assertion	jao1i	$$⊢\left(\phi \vee \psi \right)\to \left(\chi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		jao1i.1	$$⊢\psi \to \left(\chi \to \phi \right)$$
2		ax-1	$$⊢\phi \to \left(\chi \to \phi \right)$$
3	2 1	jaoi	$$⊢\left(\phi \vee \psi \right)\to \left(\chi \to \phi \right)$$