Theorem jaodd

Description: Double deduction form of jaoi . (Contributed by Steven Nguyen, 17-Jul-2022)

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

Proof

Step	Hyp	Ref	Expression
1		jaodd.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2		jaodd.2	$$⊢\phi \to \left(\psi \to \left(\tau \to \theta \right)\right)$$
3		jao	$$⊢\left(\chi \to \theta \right)\to \left(\left(\tau \to \theta \right)\to \left(\left(\chi \vee \tau \right)\to \theta \right)\right)$$
4	1 2 3	syl6c	$$⊢\phi \to \left(\psi \to \left(\left(\chi \vee \tau \right)\to \theta \right)\right)$$