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Theorem atelch 23800
Description: An atom is a Hilbert lattice element. (Contributed by NM, 22-Jun-2004.) (New usage is discouraged.)
Assertion
Ref Expression
atelch  |-  ( A  e. HAtoms  ->  A  e.  CH )

Proof of Theorem atelch
StepHypRef Expression
1 atssch 23799 . 2  |- HAtoms  C_  CH
21sseli 3304 1  |-  ( A  e. HAtoms  ->  A  e.  CH )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1721   CHcch 22385  HAtomscat 22421
This theorem is referenced by:  atsseq  23803  atcveq0  23804  chcv1  23811  chcv2  23812  hatomistici  23818  chrelati  23820  chrelat2i  23821  cvati  23822  cvexchlem  23824  cvp  23831  atnemeq0  23833  atcv0eq  23835  atcv1  23836  atexch  23837  atomli  23838  atoml2i  23839  atordi  23840  atcvatlem  23841  atcvati  23842  atcvat2i  23843  chirredlem1  23846  chirredlem2  23847  chirredlem3  23848  chirredlem4  23849  chirredi  23850  atcvat3i  23852  atcvat4i  23853  atdmd  23854  atmd  23855  atmd2  23856  atabsi  23857  mdsymlem2  23860  mdsymlem3  23861  mdsymlem5  23863  mdsymlem8  23866  atdmd2  23870  sumdmdi  23876  dmdbr4ati  23877  dmdbr5ati  23878  dmdbr6ati  23879
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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