Theorem chsh 5131

Description: A closed subspace is a subspace.

Assertion

Ref	Expression
chsh	|- (H e. CH -> H e. SH)

Proof of Theorem chsh

Step	Hyp	Ref	Expression
1		chsssh 5129	. 2 |- CH (_ SH
2	1	sseli 1504	1 |- (H e. CH -> H e. SH)

Syntax hints:   -> wi 2   e. wcel 1092  SHcsh 4967  CHcch 4968

This theorem is referenced by:  chshi 5132  ch0 5133  chss 5134  choclt 5191  chjvalt 5323  chjclt 5330  ch0let 5366  chle0t 5368  chslejt 5415  chjcomt 5423  chub1t 5424  chlubt 5426  chlej1t 5427  chlej2t 5428  spansnsht 5466  pjorth 5559  ch1dle 5749  sumdmdi 5785

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-in 1491  df-ss 1492  df-ch 5127

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