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Theorem chshii 21807
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 21804 . 2  |-  ( H  e.  CH  ->  H  e.  SH )
31, 2ax-mp 8 1  |-  H  e.  SH
Colors of variables: wff set class
Syntax hints:    e. wcel 1684   SHcsh 21508   CHcch 21509
This theorem is referenced by:  chssii  21811  helsh  21824  h0elsh  21835  hhsscms  21856  hhssbn  21857  hhsshl  21858  chocunii  21880  shsleji  21949  shjshcli  21955  pjhthlem1  21970  pjhthlem2  21971  omlsii  21982  ococi  21984  pjoc1i  22010  chne0i  22032  chocini  22033  chjcli  22036  chsleji  22037  chseli  22038  chunssji  22046  chjcomi  22047  chub1i  22048  chlubi  22050  chlej1i  22052  chlej2i  22053  h1de2bi  22133  h1de2ctlem  22134  spansnpji  22157  spanunsni  22158  h1datomi  22160  pjoml2i  22164  qlaxr3i  22215  osumi  22221  osumcor2i  22223  spansnji  22225  spansnm0i  22229  nonbooli  22230  spansncvi  22231  5oai  22240  3oalem2  22242  3oalem5  22245  3oalem6  22246  pjaddii  22254  pjmulii  22256  pjss2i  22259  pjssmii  22260  pj0i  22272  pjocini  22277  pjjsi  22279  pjpythi  22301  mayete3i  22307  mayete3iOLD  22308  pjnmopi  22728  pjimai  22756  pjclem4  22779  pj3si  22787  sto1i  22816  stlei  22820  strlem1  22830  hatomici  22939  hatomistici  22942  atomli  22962  chirredlem3  22972  sumdmdii  22995  sumdmdlem  22998  sumdmdlem2  22999
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-xp 4695  df-cnv 4697  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702  df-iota 5219  df-fv 5263  df-ov 5861  df-ch 21801
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