Mathbox for Norm Megill < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  opposet Structured version   Unicode version

Theorem opposet 29980
 Description: Every orthoposet is a poset. (Contributed by NM, 12-Oct-2011.)
Assertion
Ref Expression
opposet

Proof of Theorem opposet
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqid 2436 . . 3
2 eqid 2436 . . 3
3 eqid 2436 . . 3
4 eqid 2436 . . 3
5 eqid 2436 . . 3
6 eqid 2436 . . 3
7 eqid 2436 . . 3
81, 2, 3, 4, 5, 6, 7isopos 29978 . 2
9 simpl1 960 . 2
108, 9sylbi 188 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   w3a 936   wceq 1652   wcel 1725  wral 2705   class class class wbr 4212  cfv 5454  (class class class)co 6081  cbs 13469  cple 13536  coc 13537  cpo 14397  cjn 14401  cmee 14402  cp0 14466  cp1 14467  cops 29970 This theorem is referenced by:  op0le  29984  ople0  29985  ople1  29989  op1le  29990  opltcon3b  30002  olposN  30013  ncvr1  30070  cvrcmp2  30082  leatb  30090  dalemcea  30457 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 2417  ax-nul 4338 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 2285  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-ov 6084  df-oposet 29974
 Copyright terms: Public domain W3C validator