![]() |
Mathbox for Norm Megill |
< Previous
Next >
Nearby theorems |
|
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 38814 | . 2 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP)) | |
2 | 1 | simplbi 496 | 1 ⊢ (𝐾 ∈ OL → 𝐾 ∈ Lat) |
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: oldmm1 38819 oldmj1 38823 olj01 38827 olj02 38828 olm12 38830 latmassOLD 38831 latm12 38832 latm32 38833 latmrot 38834 latm4 38835 latmmdiN 38836 latmmdir 38837 olm01 38838 olm02 38839 omllat 38844 meetat 38898 |
Copyright terms: Public domain | W3C validator |