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Mirrors > Home > MPE Home > Th. List > Mathboxes > isolat | Structured version Visualization version GIF version |
Description: The predicate "is an ortholattice." (Contributed by NM, 18-Sep-2011.) |
Ref | Expression |
---|---|
isolat | ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ol 36313 | . 2 ⊢ OL = (Lat ∩ OP) | |
2 | 1 | elin2 4173 | 1 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 ∧ wa 398 ∈ wcel 2110 Latclat 17654 OPcops 36307 OLcol 36309 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-v 3496 df-in 3942 df-ol 36313 |
This theorem is referenced by: ollat 36348 olop 36349 isolatiN 36351 |
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