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Theorem isch 22718
 Description: Closed subspace of a Hilbert space. (Contributed by NM, 17-Aug-1999.) (Revised by Mario Carneiro, 23-Dec-2013.) (New usage is discouraged.)
Assertion
Ref Expression
isch

Proof of Theorem isch
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 oveq1 6081 . . . 4
21imaeq2d 5196 . . 3
3 id 20 . . 3
42, 3sseq12d 3370 . 2
5 df-ch 22717 . 2
64, 5elrab2 3087 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wceq 1652   wcel 1725   wss 3313  cima 4874  (class class class)co 6074   cmap 7011  cn 9993   chli 22423  csh 22424  cch 22425 This theorem is referenced by:  isch2  22719  chsh  22720 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 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-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2704  df-rab 2707  df-v 2951  df-dif 3316  df-un 3318  df-in 3320  df-ss 3327  df-nul 3622  df-if 3733  df-sn 3813  df-pr 3814  df-op 3816  df-uni 4009  df-br 4206  df-opab 4260  df-xp 4877  df-cnv 4879  df-dm 4881  df-rn 4882  df-res 4883  df-ima 4884  df-iota 5411  df-fv 5455  df-ov 6077  df-ch 22717
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