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Theorem ollat 30025
Description: An ortholattice is a lattice. (Contributed by NM, 18-Sep-2011.)
Assertion
Ref Expression
ollat  |-  ( K  e.  OL  ->  K  e.  Lat )

Proof of Theorem ollat
StepHypRef Expression
1 isolat 30024 . 2  |-  ( K  e.  OL  <->  ( K  e.  Lat  /\  K  e.  OP ) )
21simplbi 446 1  |-  ( K  e.  OL  ->  K  e.  Lat )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1696   Latclat 14167   OPcops 29984   OLcol 29986
This theorem is referenced by:  oldmm1  30029  oldmj1  30033  olj01  30037  olj02  30038  olm12  30040  latmassOLD  30041  latm12  30042  latm32  30043  latmrot  30044  latm4  30045  latmmdiN  30046  latmmdir  30047  olm01  30048  olm02  30049  omllat  30054  meetat  30108
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-ol 29990
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