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| Mirrors > Home > MPE Home > Th. List > Mathboxes > ollat | Structured version Visualization version GIF version | ||
| Description: An ortholattice is a lattice. (Contributed by NM, 18-Sep-2011.) | 
| Ref | Expression | 
|---|---|
| ollat | ⊢ (𝐾 ∈ OL → 𝐾 ∈ Lat) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | isolat 39213 | . 2 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP)) | |
| 2 | 1 | simplbi 497 | 1 ⊢ (𝐾 ∈ OL → 𝐾 ∈ Lat) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∈ wcel 2108 Latclat 18476 OPcops 39173 OLcol 39175 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-in 3958 df-ol 39179 | 
| This theorem is referenced by: oldmm1 39218 oldmj1 39222 olj01 39226 olj02 39227 olm12 39229 latmassOLD 39230 latm12 39231 latm32 39232 latmrot 39233 latm4 39234 latmmdiN 39235 latmmdir 39236 olm01 39237 olm02 39238 omllat 39243 meetat 39297 | 
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