Mathbox for Norm Megill |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > hloml | Structured version Visualization version GIF version |
Description: A Hilbert lattice is orthomodular. (Contributed by NM, 20-Oct-2011.) |
Ref | Expression |
---|---|
hloml | ⊢ (𝐾 ∈ HL → 𝐾 ∈ OML) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hlomcmcv 37013 | . 2 ⊢ (𝐾 ∈ HL → (𝐾 ∈ OML ∧ 𝐾 ∈ CLat ∧ 𝐾 ∈ CvLat)) | |
2 | 1 | simp1d 1143 | 1 ⊢ (𝐾 ∈ HL → 𝐾 ∈ OML) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2114 CLatccla 17833 OMLcoml 36832 CvLatclc 36922 HLchlt 37007 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-8 2116 ax-9 2124 ax-ext 2710 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 847 df-3an 1090 df-tru 1545 df-ex 1787 df-sb 2075 df-clab 2717 df-cleq 2730 df-clel 2811 df-ral 3058 df-rex 3059 df-rab 3062 df-v 3400 df-un 3848 df-in 3850 df-ss 3860 df-sn 4517 df-pr 4519 df-op 4523 df-uni 4797 df-br 5031 df-iota 6297 df-fv 6347 df-ov 7173 df-hlat 37008 |
This theorem is referenced by: hlol 37018 hlomcmat 37022 poml4N 37610 doca2N 38783 djajN 38794 dihoml4c 39033 |
Copyright terms: Public domain | W3C validator |