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Theorem atssch 22923
Description: Atoms are a subset of the Hilbert lattice. (Contributed by NM, 14-Aug-2002.) (New usage is discouraged.)
Assertion
Ref Expression
atssch  |- HAtoms  C_  CH

Proof of Theorem atssch
Dummy variable  x is distinct from all other variables.
StepHypRef Expression
1 df-at 22918 . 2  |- HAtoms  =  {
x  e.  CH  |  0H  <oH  x }
2 ssrab2 3258 . 2  |-  { x  e.  CH  |  0H  <oH  x }  C_  CH
31, 2eqsstri 3208 1  |- HAtoms  C_  CH
Colors of variables: wff set class
Syntax hints:   {crab 2547    C_ wss 3152   class class class wbr 4023   CHcch 21509   0Hc0h 21515    <oH ccv 21544  HAtomscat 21545
This theorem is referenced by:  atelch  22924  shatomistici  22941  hatomistici  22942  chpssati  22943
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-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-in 3159  df-ss 3166  df-at 22918
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