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Theorem olposN 29331
Description: An ortholattice is a poset. (Contributed by NM, 16-Oct-2011.) (New usage is discouraged.)
Assertion
Ref Expression
olposN  |-  ( K  e.  OL  ->  K  e.  Poset )

Proof of Theorem olposN
StepHypRef Expression
1 olop 29330 . 2  |-  ( K  e.  OL  ->  K  e.  OP )
2 opposet 29298 . 2  |-  ( K  e.  OP  ->  K  e.  Poset )
31, 2syl 16 1  |-  ( K  e.  OL  ->  K  e.  Poset )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1717   Posetcpo 14325   OPcops 29288   OLcol 29290
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369  ax-nul 4280
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2243  df-clab 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-ne 2553  df-ral 2655  df-rex 2656  df-rab 2659  df-v 2902  df-sbc 3106  df-dif 3267  df-un 3269  df-in 3271  df-ss 3278  df-nul 3573  df-if 3684  df-sn 3764  df-pr 3765  df-op 3767  df-uni 3959  df-br 4155  df-iota 5359  df-fv 5403  df-ov 6024  df-oposet 29292  df-ol 29294
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