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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 36194 | . 2 ⊢ OL = (Lat ∩ OP) | |
2 | 1 | elin2 4171 | 1 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 207 ∧ wa 396 ∈ wcel 2105 Latclat 17643 OPcops 36188 OLcol 36190 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-v 3494 df-in 3940 df-ol 36194 |
This theorem is referenced by: ollat 36229 olop 36230 isolatiN 36232 |
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