Theorem orcomdd

Description: Commutativity of logic disjunction, in double deduction form. Should not be moved to main, see PR #3034 in Github. Use orcomd instead. (Contributed by Giovanni Mascellani, 19-Mar-2018) (New usage is discouraged.) (Proof modification is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		orcomdd.1	$$⊢\phi \to \left(\psi \to \left(\chi \vee \theta \right)\right)$$
2		pm1.4	$$⊢\left(\chi \vee \theta \right)\to \left(\theta \vee \chi \right)$$
3	1 2	syl6	$$⊢\phi \to \left(\psi \to \left(\theta \vee \chi \right)\right)$$