| 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 39213 | . 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 2108 Latclat 18476 OPcops 39173 OLcol 39175 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-in 3958 df-ol 39179 |
| This theorem is referenced by: (None) |
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