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Mathbox for Norm Megill |
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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 35253 | . 2 ⊢ OL = (Lat ∩ OP) | |
2 | 1 | elin2 4028 | 1 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 198 ∧ wa 386 ∈ wcel 2166 Latclat 17398 OPcops 35247 OLcol 35249 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1896 ax-4 1910 ax-5 2011 ax-6 2077 ax-7 2114 ax-9 2175 ax-10 2194 ax-11 2209 ax-12 2222 ax-ext 2803 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 881 df-tru 1662 df-ex 1881 df-nf 1885 df-sb 2070 df-clab 2812 df-cleq 2818 df-clel 2821 df-nfc 2958 df-v 3416 df-in 3805 df-ol 35253 |
This theorem is referenced by: ollat 35288 olop 35289 isolatiN 35291 |
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