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Theorem olposN 29950
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 29949 . 2  |-  ( K  e.  OL  ->  K  e.  OP )
2 opposet 29917 . 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 1725   Posetcpo 14389   OPcops 29907   OLcol 29909
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-nul 4330
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076  df-oposet 29911  df-ol 29913
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