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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.) |
Ref | Expression |
---|---|
3orcomb | ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orcom 401 | . . 3 ⊢ ((𝜓 ∨ 𝜒) ↔ (𝜒 ∨ 𝜓)) | |
2 | 1 | orbi2i 540 | . 2 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) ↔ (𝜑 ∨ (𝜒 ∨ 𝜓))) |
3 | 3orass 1034 | . 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒))) | |
4 | 3orass 1034 | . 2 ⊢ ((𝜑 ∨ 𝜒 ∨ 𝜓) ↔ (𝜑 ∨ (𝜒 ∨ 𝜓))) | |
5 | 2, 3, 4 | 3bitr4i 291 | 1 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 195 ∨ wo 382 ∨ w3o 1030 |
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 196 df-or 384 df-3or 1032 |
This theorem is referenced by: eueq3 3348 swoso 7662 swrdnd 13284 colcom 25253 legso 25294 lncom 25317 soseq 30995 colinearperm1 31339 frege129d 37074 ordelordALT 37768 ordelordALTVD 38125 |
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