Theorem orcomdd 38191

Description: Commutativity of logic disjunction, in double deduction form. Should not be moved to main, see PR #3034 in Github. Use orcomd 871 instead. (Contributed by Giovanni Mascellani, 19-Mar-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
orcomdd.1	⊢ (𝜑 → (𝜓 → (𝜒 ∨ 𝜃)))

Assertion

Ref	Expression
orcomdd	⊢ (𝜑 → (𝜓 → (𝜃 ∨ 𝜒)))

Proof of Theorem orcomdd

Step	Hyp	Ref	Expression
1		orcomdd.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 ∨ 𝜃)))
2		pm1.4 869	. 2 ⊢ ((𝜒 ∨ 𝜃) → (𝜃 ∨ 𝜒))
3	1, 2	syl6 35	1 ⊢ (𝜑 → (𝜓 → (𝜃 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 847

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-or 848

This theorem is referenced by: (None)