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Theorem chshii 24645
Description: A closed subspace is a subspace. (Contributed by NM, 19-Oct-1999.) (New usage is discouraged.)
Hypothesis
Ref Expression
chshi.1  |-  H  e. 
CH
Assertion
Ref Expression
chshii  |-  H  e.  SH

Proof of Theorem chshii
StepHypRef Expression
1 chshi.1 . 2  |-  H  e. 
CH
2 chsh 24642 . 2  |-  ( H  e.  CH  ->  H  e.  SH )
31, 2ax-mp 5 1  |-  H  e.  SH
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1756   SHcsh 24345   CHcch 24346
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2577  df-rex 2736  df-rab 2739  df-v 2989  df-dif 3346  df-un 3348  df-in 3350  df-ss 3357  df-nul 3653  df-if 3807  df-sn 3893  df-pr 3895  df-op 3899  df-uni 4107  df-br 4308  df-opab 4366  df-xp 4861  df-cnv 4863  df-dm 4865  df-rn 4866  df-res 4867  df-ima 4868  df-iota 5396  df-fv 5441  df-ov 6109  df-ch 24639
This theorem is referenced by:  chssii  24649  helsh  24663  h0elsh  24674  hhsscms  24695  hhssbn  24696  hhsshl  24697  chocunii  24719  shsleji  24788  shjshcli  24794  pjhthlem1  24809  pjhthlem2  24810  omlsii  24821  ococi  24823  pjoc1i  24849  chne0i  24871  chocini  24872  chjcli  24875  chsleji  24876  chseli  24877  chunssji  24885  chjcomi  24886  chub1i  24887  chlubi  24889  chlej1i  24891  chlej2i  24892  h1de2bi  24972  h1de2ctlem  24973  spansnpji  24996  spanunsni  24997  h1datomi  24999  pjoml2i  25003  qlaxr3i  25054  osumi  25060  osumcor2i  25062  spansnji  25064  spansnm0i  25068  nonbooli  25069  spansncvi  25070  5oai  25079  3oalem2  25081  3oalem5  25084  3oalem6  25085  pjaddii  25093  pjmulii  25095  pjss2i  25098  pjssmii  25099  pj0i  25111  pjocini  25116  pjjsi  25118  pjpythi  25140  mayete3i  25146  mayete3iOLD  25147  pjnmopi  25567  pjimai  25595  pjclem4  25618  pj3si  25626  sto1i  25655  stlei  25659  strlem1  25669  hatomici  25778  hatomistici  25781  atomli  25801  chirredlem3  25811  sumdmdii  25834  sumdmdlem  25837  sumdmdlem2  25838
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