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Theorem atssch 23847
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 23842 . 2  |- HAtoms  =  {
x  e.  CH  |  0H  <oH  x }
2 ssrab2 3429 . 2  |-  { x  e.  CH  |  0H  <oH  x }  C_  CH
31, 2eqsstri 3379 1  |- HAtoms  C_  CH
Colors of variables: wff set class
Syntax hints:   {crab 2710    C_ wss 3321   class class class wbr 4213   CHcch 22433   0Hc0h 22439    <oH ccv 22468  HAtomscat 22469
This theorem is referenced by:  atelch  23848  shatomistici  23865  hatomistici  23866  chpssati  23867
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-rab 2715  df-in 3328  df-ss 3335  df-at 23842
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