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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 37453 | . 2 ⊢ OL = (Lat ∩ OP) | |
2 | 1 | elin2 4144 | 1 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∧ wa 396 ∈ wcel 2105 Latclat 18246 OPcops 37447 OLcol 37449 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-ext 2707 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1543 df-ex 1781 df-sb 2067 df-clab 2714 df-cleq 2728 df-clel 2814 df-v 3443 df-in 3905 df-ol 37453 |
This theorem is referenced by: ollat 37488 olop 37489 isolatiN 37491 |
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