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Theorem atssch 31596
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

Proof of Theorem atssch
Dummy variable 𝑥 is distinct from all other variables.
StepHypRef Expression
1 df-at 31591 . 2 HAtoms = {𝑥C ∣ 0 𝑥}
21ssrab3 4081 1 HAtoms ⊆ C
Colors of variables: wff setvar class
Syntax hints:  wss 3949   class class class wbr 5149   C cch 30182  0c0h 30188   ccv 30217  HAtomscat 30218
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3434  df-v 3477  df-in 3956  df-ss 3966  df-at 31591
This theorem is referenced by:  atelch  31597  shatomistici  31614  hatomistici  31615  chpssati  31616
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