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Theorem or32dd 32866
Description: A rearrangement of disjuncts, in double deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)
Hypothesis
Ref Expression
or32dd.1 (𝜑 → (𝜓 → ((𝜒𝜃) ∨ 𝜏)))
Assertion
Ref Expression
or32dd (𝜑 → (𝜓 → ((𝜒𝜏) ∨ 𝜃)))

Proof of Theorem or32dd
StepHypRef Expression
1 or32dd.1 . 2 (𝜑 → (𝜓 → ((𝜒𝜃) ∨ 𝜏)))
2 or32 547 . 2 (((𝜒𝜏) ∨ 𝜃) ↔ ((𝜒𝜃) ∨ 𝜏))
31, 2syl6ibr 240 1 (𝜑 → (𝜓 → ((𝜒𝜏) ∨ 𝜃)))
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:  mpt2bi123f  32941  mptbi12f  32945  ac6s6  32950
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