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Theorem riotaocN 34024
 Description: The orthocomplement of the unique poset element such that . (riotaneg 10518 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 2629 . . 3
2 nfriota1 6252 . . 3
31, 2nffv 5873 . 2
4 riotaoc.b . . 3
5 riotaoc.o . . 3
64, 5opoccl 34009 . 2
74, 5opoccl 34009 . 2
8 riotaoc.a . 2
9 fveq2 5866 . 2
104, 5opoccl 34009 . . 3
114, 5opcon2b 34012 . . 3
1210, 11reuhypd 4674 . 2
133, 6, 7, 8, 9, 12riotaxfrd 6276 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1379   wcel 1767  wreu 2816  cfv 5588  crio 6244  cbs 14490  coc 14563  cops 33987 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-nul 4576 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-reu 2821  df-rmo 2822  df-rab 2823  df-v 3115  df-sbc 3332  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-uni 4246  df-br 4448  df-dm 5009  df-iota 5551  df-fv 5596  df-riota 6245  df-ov 6287  df-oposet 33991 This theorem is referenced by:  glbconN  34191
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