Theorem orcomdd 33061

Description: Commutativity of logic disjunction, in double deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)

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		pm1.4 400	. 2 ⊢ ((𝜒 ∨ 𝜃) → (𝜃 ∨ 𝜒))
3	1, 2	syl6 34	1 ⊢ (𝜑 → (𝜓 → (𝜃 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 382

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 196  df-or 384

This theorem is referenced by:  cnf2dd  33063