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Mirrors > Home > MPE Home > Th. List > Mathboxes > or32dd | Structured version Visualization version GIF version |
Description: A rearrangement of disjuncts, in double deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.) |
Ref | Expression |
---|---|
or32dd.1 | ⊢ (𝜑 → (𝜓 → ((𝜒 ∨ 𝜃) ∨ 𝜏))) |
Ref | Expression |
---|---|
or32dd | ⊢ (𝜑 → (𝜓 → ((𝜒 ∨ 𝜏) ∨ 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | or32dd.1 | . 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∨ 𝜃) ∨ 𝜏))) | |
2 | or32 923 | . 2 ⊢ (((𝜒 ∨ 𝜏) ∨ 𝜃) ↔ ((𝜒 ∨ 𝜃) ∨ 𝜏)) | |
3 | 1, 2 | syl6ibr 251 | 1 ⊢ (𝜑 → (𝜓 → ((𝜒 ∨ 𝜏) ∨ 𝜃))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 844 |
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 206 df-or 845 |
This theorem is referenced by: mpobi123f 36316 mptbi12f 36320 ac6s6 36326 |
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