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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 39193 | . 2 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP)) | |
4 | 1, 2, 3 | mpbir2an 711 | 1 ⊢ 𝐾 ∈ OL |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2105 Latclat 18488 OPcops 39153 OLcol 39155 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-ext 2705 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1539 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-clel 2813 df-v 3479 df-in 3969 df-ol 39159 |
This theorem is referenced by: (None) |
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