Mathbox for Norm Megill < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  isolatiN Structured version   Visualization version   GIF version

Theorem isolatiN 35372
 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 35368 . 2 (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
41, 2, 3mpbir2an 701 1 𝐾 ∈ OL
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2107  Latclat 17431  OPcops 35328  OLcol 35330 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-ext 2754 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-nfc 2921  df-v 3400  df-in 3799  df-ol 35334 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator