Theorem atssch 10354

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 10349	. 2 |- Atoms = {x e. CH | 0H <o x}
2		ssrab2 2182	. 2 |- {x e. CH | 0H <o x} (_ CH
3	1, 2	eqsstri 2142	1 |- Atoms (_ CH

Syntax hints:  {crab 1695   (_ wss 2098   class class class wbr 2674  CHcch 8881  0Hc0h 8887  Atomscat 8916   <o ccv 8917

This theorem is referenced by:  atelch 10355  shatomistici 10372  hatomistici 10373  chpssati 10374

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1003  ax-gen 1004  ax-8 1005  ax-10 1007  ax-12 1009  ax-17 1012  ax-4 1014  ax-5o 1016  ax-6o 1019  ax-9o 1164  ax-10o 1182  ax-16 1252  ax-11o 1260  ax-ext 1504

This theorem depends on definitions:  df-bi 154  df-an 232  df-ex 1022  df-sb 1214  df-clab 1510  df-cleq 1515  df-clel 1518  df-rab 1699  df-in 2102  df-ss 2104  df-at 10349

Copyright terms: Public domain