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Theorem ocval 22772
 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 22492 . . 3
21elpw2 4356 . 2
3 raleq 2896 . . . 4
43rabbidv 2940 . . 3
5 df-oc 22744 . . 3
61rabex 4346 . . 3
74, 5, 6fvmpt 5798 . 2
82, 7sylbir 205 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  wral 2697  crab 2701   wss 3312  cpw 3791  cfv 5446  (class class class)co 6073  cc0 8980  chil 22412   csp 22415  cort 22423 This theorem is referenced by:  ocel  22773  ocsh  22775  occon  22779  chocvali  22791 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-hilex 22492 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-iota 5410  df-fun 5448  df-fv 5454  df-oc 22744
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