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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 38814 | . 2 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP)) | |
2 | 1 | simprbi 495 | 1 ⊢ (𝐾 ∈ OL → 𝐾 ∈ OP) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2098 Latclat 18426 OPcops 38774 OLcol 38776 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2696 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2703 df-cleq 2717 df-clel 2802 df-v 3463 df-in 3951 df-ol 38780 |
This theorem is referenced by: olposN 38817 oldmm1 38819 oldmm2 38820 oldmm3N 38821 oldmm4 38822 oldmj1 38823 oldmj2 38824 oldmj3 38825 oldmj4 38826 olj01 38827 olj02 38828 olm11 38829 olm12 38830 latmassOLD 38831 olm01 38838 olm02 38839 omlop 38843 meetat 38898 hlop 38964 polatN 39534 |
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