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Theorem ocel 22784
 Description: Membership in orthogonal complement of H subset. (Contributed by NM, 7-Aug-2000.) (New usage is discouraged.)
Assertion
Ref Expression
ocel
Distinct variable groups:   ,   ,

Proof of Theorem ocel
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ocval 22783 . . 3
21eleq2d 2504 . 2
3 oveq1 6089 . . . . 5
43eqeq1d 2445 . . . 4
54ralbidv 2726 . . 3
65elrab 3093 . 2
72, 6syl6bb 254 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726  wral 2706  crab 2710   wss 3321  cfv 5455  (class class class)co 6082  cc0 8991  chil 22423   csp 22426  cort 22434 This theorem is referenced by:  shocel  22785  ocsh  22786  ocorth  22794  ococss  22796  occllem  22806  occl  22807  chocnul  22831  h1deoi  23052  h1dei  23053  hmopidmpji  23656 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404  ax-hilex 22503 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2286  df-mo 2287  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-sbc 3163  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-pw 3802  df-sn 3821  df-pr 3822  df-op 3824  df-uni 4017  df-br 4214  df-opab 4268  df-mpt 4269  df-id 4499  df-xp 4885  df-rel 4886  df-cnv 4887  df-co 4888  df-dm 4889  df-iota 5419  df-fun 5457  df-fv 5463  df-ov 6085  df-oc 22755
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