Theorem atssch 10207

Description: Atoms are a subset of the Hilbert lattice.

Assertion

Ref	Expression
atssch	|- Atoms (_ CH

Proof of Theorem atssch

Step	Hyp	Ref	Expression
1		df-at 10202	. 2 |- Atoms = {x e. CH | 0H <o x}
2		ssrab2 2127	. 2 |- {x e. CH | 0H <o x} (_ CH
3	1, 2	eqsstr 2087	1 |- Atoms (_ CH

Syntax hints:  {crab 1645   (_ wss 2043   class class class wbr 2614  CHcch 8737  0Hc0h 8743  Atomscat 8772   <o ccv 8773

This theorem is referenced by:  atelch 10208  shatomistic 10225  hatomistic 10226  chpssat 10227

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-rab 1649  df-in 2047  df-ss 2049  df-at 10202

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