Theorem atssch 10270

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 10265	. 2 |- Atoms = {x e. CH | 0H <o x}
2		ssrab2 2131	. 2 |- {x e. CH | 0H <o x} (_ CH
3	1, 2	eqsstr 2091	1 |- Atoms (_ CH

Syntax hints:  {crab 1648   (_ wss 2047   class class class wbr 2619  CHcch 8798  0Hc0h 8804  Atomscat 8833   <o ccv 8834

This theorem is referenced by:  atelch 10271  shatomistic 10288  hatomistic 10289  chpssat 10290

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-rab 1652  df-in 2051  df-ss 2053  df-at 10265

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