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Theorem isolatiN 39197
Description: Properties that determine an ortholattice. (Contributed by NM, 18-Sep-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
isolati.1 𝐾 ∈ Lat
isolati.2 𝐾 ∈ OP
Assertion
Ref Expression
isolatiN 𝐾 ∈ OL

Proof of Theorem isolatiN
StepHypRef Expression
1 isolati.1 . 2 𝐾 ∈ Lat
2 isolati.2 . 2 𝐾 ∈ OP
3 isolat 39193 . 2 (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
41, 2, 3mpbir2an 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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