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Theorem atssch 23799
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 23794 . 2  |- HAtoms  =  {
x  e.  CH  |  0H  <oH  x }
2 ssrab2 3388 . 2  |-  { x  e.  CH  |  0H  <oH  x }  C_  CH
31, 2eqsstri 3338 1  |- HAtoms  C_  CH
Colors of variables: wff set class
Syntax hints:   {crab 2670    C_ wss 3280   class class class wbr 4172   CHcch 22385   0Hc0h 22391    <oH ccv 22420  HAtomscat 22421
This theorem is referenced by:  atelch  23800  shatomistici  23817  hatomistici  23818  chpssati  23819
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-rab 2675  df-in 3287  df-ss 3294  df-at 23794
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