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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 34499 | . 2 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP)) | |
2 | 1 | simplbi 476 | 1 ⊢ (𝐾 ∈ OL → 𝐾 ∈ Lat) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 1990 Latclat 17045 OPcops 34459 OLcol 34461 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-in 3581 df-ol 34465 |
This theorem is referenced by: oldmm1 34504 oldmj1 34508 olj01 34512 olj02 34513 olm12 34515 latmassOLD 34516 latm12 34517 latm32 34518 latmrot 34519 latm4 34520 latmmdiN 34521 latmmdir 34522 olm01 34523 olm02 34524 omllat 34529 meetat 34583 |
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