Theorem jaod

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

	Ref	Expression
Hypotheses	jaod.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	jaod.2	$$⊢\phi \to \left(\theta \to \chi \right)$$
Assertion	jaod	$$⊢\phi \to \left(\left(\psi \vee \theta \right)\to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		jaod.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		jaod.2	$$⊢\phi \to \left(\theta \to \chi \right)$$
3	1	com12	$$⊢\psi \to \left(\phi \to \chi \right)$$
4	2	com12	$$⊢\theta \to \left(\phi \to \chi \right)$$
5	3 4	jaoi	$$⊢\left(\psi \vee \theta \right)\to \left(\phi \to \chi \right)$$
6	5	com12	$$⊢\phi \to \left(\left(\psi \vee \theta \right)\to \chi \right)$$