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

Theorem ollat 39214
Description: An ortholattice is a lattice. (Contributed by NM, 18-Sep-2011.)
Assertion
Ref Expression
ollat (𝐾 ∈ OL → 𝐾 ∈ Lat)

Proof of Theorem ollat
StepHypRef Expression
1 isolat 39213 . 2 (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
21simplbi 497 1 (𝐾 ∈ OL → 𝐾 ∈ Lat)
Colors of variables: wff setvar class
Syntax hints:  wi 4  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:  oldmm1  39218  oldmj1  39222  olj01  39226  olj02  39227  olm12  39229  latmassOLD  39230  latm12  39231  latm32  39232  latmrot  39233  latm4  39234  latmmdiN  39235  latmmdir  39236  olm01  39237  olm02  39238  omllat  39243  meetat  39297
  Copyright terms: Public domain W3C validator