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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 1094 | . 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜓 ∨ 𝜑 ∨ 𝜒)) | |
2 | 3orrot 1093 | . 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 205 ∨ w3o 1087 |
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 847 df-3or 1089 |
This theorem is referenced by: eueq3 3668 soseq 8084 swoso 8640 swrdnd 14500 colcom 27329 legso 27370 lncom 27393 colinearperm1 34579 oneltri 41495 frege129d 41940 ordelordALT 42724 ordelordALTVD 43054 |
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