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Mathbox for Norm Megill |
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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 35932 | . 2 ⊢ (𝐾 ∈ OML → 𝐾 ∈ OL) | |
2 | olop 35906 | . 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 2081 OPcops 35864 OLcol 35866 OMLcoml 35867 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1777 ax-4 1791 ax-5 1888 ax-6 1947 ax-7 1992 ax-8 2083 ax-9 2091 ax-10 2112 ax-11 2126 ax-12 2141 ax-ext 2769 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 843 df-3an 1082 df-tru 1525 df-ex 1762 df-nf 1766 df-sb 2043 df-clab 2776 df-cleq 2788 df-clel 2863 df-nfc 2935 df-ral 3110 df-rex 3111 df-rab 3114 df-v 3439 df-dif 3866 df-un 3868 df-in 3870 df-ss 3878 df-nul 4216 df-if 4386 df-sn 4477 df-pr 4479 df-op 4483 df-uni 4750 df-br 4967 df-iota 6194 df-fv 6238 df-ov 7024 df-ol 35870 df-oml 35871 |
This theorem is referenced by: omllaw2N 35936 omllaw4 35938 cmtcomlemN 35940 cmt2N 35942 cmt3N 35943 cmt4N 35944 cmtbr2N 35945 cmtbr3N 35946 cmtbr4N 35947 lecmtN 35948 omlfh1N 35950 omlfh3N 35951 omlspjN 35953 atlatmstc 36011 |
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