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Theorem h1deoi 23052
 Description: Membership in orthocomplement of 1-dimensional subspace. (Contributed by NM, 7-Jul-2001.) (New usage is discouraged.)
Hypothesis
Ref Expression
h1deot.1
Assertion
Ref Expression
h1deoi

Proof of Theorem h1deoi
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 h1deot.1 . . 3
2 snssi 3943 . . 3
3 ocel 22784 . . 3
41, 2, 3mp2b 10 . 2
51elexi 2966 . . . 4
6 oveq2 6090 . . . . 5
76eqeq1d 2445 . . . 4
85, 7ralsn 3850 . . 3
98anbi2i 677 . 2
104, 9bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wceq 1653   wcel 1726  wral 2706   wss 3321  csn 3815  cfv 5455  (class class class)co 6082  cc0 8991  chil 22423   csp 22426  cort 22434 This theorem is referenced by:  h1dei  23053 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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