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Theorem chelii 26446
Description: A member of a closed subspace of a Hilbert space is a vector. (Contributed by NM, 6-Oct-1999.) (New usage is discouraged.)
Hypotheses
Ref Expression
chssi.1  |-  H  e. 
CH
cheli.1  |-  A  e.  H
Assertion
Ref Expression
chelii  |-  A  e. 
~H

Proof of Theorem chelii
StepHypRef Expression
1 chssi.1 . . 3  |-  H  e. 
CH
21chssii 26444 . 2  |-  H  C_  ~H
3 cheli.1 . 2  |-  A  e.  H
42, 3sselii 3436 1  |-  A  e. 
~H
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1840   ~Hchil 26131   CHcch 26141
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650  ax-5 1723  ax-6 1769  ax-7 1812  ax-10 1859  ax-11 1864  ax-12 1876  ax-13 2024  ax-ext 2378  ax-sep 4514  ax-hilex 26211
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 974  df-tru 1406  df-ex 1632  df-nf 1636  df-sb 1762  df-clab 2386  df-cleq 2392  df-clel 2395  df-nfc 2550  df-rex 2757  df-rab 2760  df-v 3058  df-dif 3414  df-un 3416  df-in 3418  df-ss 3425  df-nul 3736  df-if 3883  df-pw 3954  df-sn 3970  df-pr 3972  df-op 3976  df-uni 4189  df-br 4393  df-opab 4451  df-xp 4946  df-cnv 4948  df-dm 4950  df-rn 4951  df-res 4952  df-ima 4953  df-iota 5487  df-fv 5531  df-ov 6235  df-sh 26419  df-ch 26434
This theorem is referenced by: (None)
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