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Theorem atssch 29511
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 29506 . 2 HAtoms = {𝑥C ∣ 0 𝑥}
2 ssrab2 3828 . 2 {𝑥C ∣ 0 𝑥} ⊆ C
31, 2eqsstri 3776 1 HAtoms ⊆ C
Colors of variables: wff setvar class
Syntax hints:  {crab 3054  wss 3715   class class class wbr 4804   C cch 28095  0c0h 28101   ccv 28130  HAtomscat 28131
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-rab 3059  df-in 3722  df-ss 3729  df-at 29506
This theorem is referenced by:  atelch  29512  shatomistici  29529  hatomistici  29530  chpssati  29531
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