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Theorem riotaocN 30007
 Description: The orthocomplement of the unique poset element such that . (riotaneg 9983 analog.) (Contributed by NM, 16-Jan-2012.) (New usage is discouraged.)
Hypotheses
Ref Expression
riotaoc.b
riotaoc.o
riotaoc.a
Assertion
Ref Expression
riotaocN
Distinct variable groups:   ,,   ,,   , ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem riotaocN
StepHypRef Expression
1 nfcv 2572 . . 3
2 nfriota1 6557 . . 3
31, 2nffv 5735 . 2
4 riotaoc.b . . 3
5 riotaoc.o . . 3
64, 5opoccl 29992 . 2
74, 5opoccl 29992 . 2
8 riotaoc.a . 2
9 fveq2 5728 . 2
104, 5opoccl 29992 . . 3
114, 5opcon2b 29995 . . 3
1210, 11reuhypd 4750 . 2
133, 6, 7, 8, 9, 12riotaxfrd 6581 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  wreu 2707  cfv 5454  crio 6542  cbs 13469  coc 13537  cops 29970 This theorem is referenced by:  glbconN  30174 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-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-reu 2712  df-rmo 2713  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-riota 6549  df-oposet 29974
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