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Theorem riotaocN 29468
 Description: The orthocomplement of the unique poset element such that . (riotaneg 9819 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 2494 . . 3
2 nfriota1 6399 . . 3
31, 2nffv 5615 . 2
4 riotaoc.b . . 3
5 riotaoc.o . . 3
64, 5opoccl 29453 . 2
74, 5opoccl 29453 . 2
8 riotaoc.a . 2
9 fveq2 5608 . 2
104, 5opoccl 29453 . . 3
114, 5opcon2b 29456 . . 3
1210, 11reuhypd 4643 . 2
133, 6, 7, 8, 9, 12riotaxfrd 6423 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358   wceq 1642   wcel 1710  wreu 2621  cfv 5337  crio 6384  cbs 13245  coc 13313  cops 29431 This theorem is referenced by:  glbconN  29635 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-nul 4230 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2213  df-mo 2214  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-ral 2624  df-rex 2625  df-reu 2626  df-rmo 2627  df-rab 2628  df-v 2866  df-sbc 3068  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-op 3725  df-uni 3909  df-br 4105  df-iota 5301  df-fv 5345  df-ov 5948  df-riota 6391  df-oposet 29435
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