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	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 ∨ 𝜃 ) ) )
Assertion	orcomdd	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 ∨ 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		orcomdd.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 ∨ 𝜃 ) ) )
2		pm1.4	⊢ ( ( 𝜒 ∨ 𝜃 ) → ( 𝜃 ∨ 𝜒 ) )
3	1 2	syl6	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 ∨ 𝜒 ) ) )