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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 34499 | . 2 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP)) | |
4 | 1, 2, 3 | mpbir2an 955 | 1 ⊢ 𝐾 ∈ OL |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1990 Latclat 17045 OPcops 34459 OLcol 34461 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-in 3581 df-ol 34465 |
This theorem is referenced by: (None) |
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