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Mirrors > Home > MPE Home > Th. List > Mathboxes > omlop | Structured version Visualization version GIF version |
Description: An orthomodular lattice is an orthoposet. (Contributed by NM, 6-Nov-2011.) |
Ref | Expression |
---|---|
omlop | ⊢ (𝐾 ∈ OML → 𝐾 ∈ OP) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | omlol 36378 | . 2 ⊢ (𝐾 ∈ OML → 𝐾 ∈ OL) | |
2 | olop 36352 | . 2 ⊢ (𝐾 ∈ OL → 𝐾 ∈ OP) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝐾 ∈ OML → 𝐾 ∈ OP) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2114 OPcops 36310 OLcol 36312 OMLcoml 36313 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-ral 3145 df-rab 3149 df-v 3498 df-dif 3941 df-un 3943 df-in 3945 df-ss 3954 df-nul 4294 df-if 4470 df-sn 4570 df-pr 4572 df-op 4576 df-uni 4841 df-br 5069 df-iota 6316 df-fv 6365 df-ov 7161 df-ol 36316 df-oml 36317 |
This theorem is referenced by: omllaw2N 36382 omllaw4 36384 cmtcomlemN 36386 cmt2N 36388 cmt3N 36389 cmt4N 36390 cmtbr2N 36391 cmtbr3N 36392 cmtbr4N 36393 lecmtN 36394 omlfh1N 36396 omlfh3N 36397 omlspjN 36399 atlatmstc 36457 |
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