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Theorem orcomdd 32859
Description: Commutativity of logic disjunction, in double deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)
Hypothesis
Ref Expression
orcomdd.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
orcomdd (𝜑 → (𝜓 → (𝜃𝜒)))

Proof of Theorem orcomdd
StepHypRef Expression
1 orcomdd.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 pm1.4 399 . 2 ((𝜒𝜃) → (𝜃𝜒))
31, 2syl6 34 1 (𝜑 → (𝜓 → (𝜃𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 381
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 195  df-or 383
This theorem is referenced by:  cnf2dd  32861
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