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| Mirrors > Home > MPE Home > Th. List > 3orcomb | Structured version Visualization version GIF version | ||
| Description: Commutation law for triple disjunction. (Contributed by Scott Fenton, 20-Apr-2011.) (Proof shortened by Wolf Lammen, 8-Apr-2022.) |
| Ref | Expression |
|---|---|
| 3orcomb | ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3orcoma 1093 | . 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜓 ∨ 𝜑 ∨ 𝜒)) | |
| 2 | 3orrot 1092 | . 2 ⊢ ((𝜓 ∨ 𝜑 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓)) | |
| 3 | 1, 2 | bitri 275 | 1 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓)) |
| Colors of variables: wff setvar class |
| Syntax hints: ↔ wb 206 ∨ w3o 1086 |
| 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 207 df-or 849 df-3or 1088 |
| This theorem is referenced by: eueq3 3717 soseq 8184 swoso 8779 swrdnd 14692 elnnzs 28387 colcom 28566 legso 28607 lncom 28630 colinearperm1 36063 oneltri 43270 frege129d 43776 ordelordALT 44557 ordelordALTVD 44887 usgrexmpl2nb3 47993 |
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