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Theorem chocvali 21708
 Description: Value of the orthogonal complement of a Hilbert lattice element. The orthogonal complement of is the set of vectors that are orthogonal to all vectors in . (Contributed by NM, 8-Aug-2004.) (New usage is discouraged.)
Hypothesis
Ref Expression
chocval.1
Assertion
Ref Expression
chocvali
Distinct variable group:   ,,

Proof of Theorem chocvali
StepHypRef Expression
1 chocval.1 . . 3
21chssii 21641 . 2
3 ocval 21689 . 2
42, 3ax-mp 10 1
 Colors of variables: wff set class Syntax hints:   wceq 1619   wcel 1621  wral 2509  crab 2512   wss 3078  cfv 4592  (class class class)co 5710  cc0 8617  chil 21329   csp 21332  cch 21339  cort 21340 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108  ax-hilex 21409 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118  df-mo 2119  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2513  df-rex 2514  df-rab 2516  df-v 2729  df-sbc 2922  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-pw 3532  df-sn 3550  df-pr 3551  df-op 3553  df-uni 3728  df-br 3921  df-opab 3975  df-mpt 3976  df-id 4202  df-xp 4594  df-rel 4595  df-cnv 4596  df-co 4597  df-dm 4598  df-rn 4599  df-res 4600  df-ima 4601  df-fun 4602  df-fv 4608  df-ov 5713  df-sh 21616  df-ch 21631  df-oc 21661
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