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Theorem ocval 26012
 Description: Value of orthogonal complement of a subset of Hilbert space. (Contributed by NM, 7-Aug-2000.) (Revised by Mario Carneiro, 23-Dec-2013.) (New usage is discouraged.)
Assertion
Ref Expression
ocval
Distinct variable group:   ,,

Proof of Theorem ocval
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-hilex 25730 . . 3
21elpw2 4617 . 2
3 raleq 3063 . . . 4
43rabbidv 3110 . . 3
5 df-oc 25984 . . 3
61rabex 4604 . . 3
74, 5, 6fvmpt 5957 . 2
82, 7sylbir 213 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1379   wcel 1767  wral 2817  crab 2821   wss 3481  cpw 4016  cfv 5594  (class class class)co 6295  cc0 9504  chil 25650   csp 25653  cort 25661 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-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pr 4692  ax-hilex 25730 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 2822  df-rex 2823  df-rab 2826  df-v 3120  df-sbc 3337  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-pw 4018  df-sn 4034  df-pr 4036  df-op 4040  df-uni 4252  df-br 4454  df-opab 4512  df-mpt 4513  df-id 4801  df-xp 5011  df-rel 5012  df-cnv 5013  df-co 5014  df-dm 5015  df-iota 5557  df-fun 5596  df-fv 5602  df-oc 25984 This theorem is referenced by:  ocel  26013  ocsh  26015  occon  26019  chocvali  26031
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