| Mathbox for Norm Megill |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > olop | Structured version Visualization version GIF version | ||
| Description: An ortholattice is an orthoposet. (Contributed by NM, 18-Sep-2011.) |
| Ref | Expression |
|---|---|
| olop | ⊢ (𝐾 ∈ OL → 𝐾 ∈ OP) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | isolat 39213 | . 2 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP)) | |
| 2 | 1 | simprbi 496 | 1 ⊢ (𝐾 ∈ OL → 𝐾 ∈ OP) |
| 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: olposN 39216 oldmm1 39218 oldmm2 39219 oldmm3N 39220 oldmm4 39221 oldmj1 39222 oldmj2 39223 oldmj3 39224 oldmj4 39225 olj01 39226 olj02 39227 olm11 39228 olm12 39229 latmassOLD 39230 olm01 39237 olm02 39238 omlop 39242 meetat 39297 hlop 39363 polatN 39933 |
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