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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > isolatiN | Structured version Visualization version GIF version |
Description: Properties that determine an ortholattice. (Contributed by NM, 18-Sep-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
isolati.1 | ⊢ 𝐾 ∈ Lat |
isolati.2 | ⊢ 𝐾 ∈ OP |
Ref | Expression |
---|---|
isolatiN | ⊢ 𝐾 ∈ OL |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isolati.1 | . 2 ⊢ 𝐾 ∈ Lat | |
2 | isolati.2 | . 2 ⊢ 𝐾 ∈ OP | |
3 | isolat 35368 | . 2 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP)) | |
4 | 1, 2, 3 | mpbir2an 701 | 1 ⊢ 𝐾 ∈ OL |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2107 Latclat 17431 OPcops 35328 OLcol 35330 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2055 ax-9 2116 ax-10 2135 ax-11 2150 ax-12 2163 ax-ext 2754 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 837 df-tru 1605 df-ex 1824 df-nf 1828 df-sb 2012 df-clab 2764 df-cleq 2770 df-clel 2774 df-nfc 2921 df-v 3400 df-in 3799 df-ol 35334 |
This theorem is referenced by: (None) |
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