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Theorem orcomdd 35481
Description: Commutativity of logic disjunction, in double deduction form. Should not be moved to main, see PR #3034 in Github. Use orcomd 867 instead. (Contributed by Giovanni Mascellani, 19-Mar-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
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 pm1.4 865 . 2 ((𝜒𝜃) → (𝜃𝜒))
31, 2syl6 35 1 (𝜑 → (𝜓 → (𝜃𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 843
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 209  df-or 844
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator