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Theorem atcv0 23850
Description: An atom covers the zero subspace. (Contributed by NM, 26-Jun-2004.) (New usage is discouraged.)
Assertion
Ref Expression
atcv0  |-  ( A  e. HAtoms  ->  0H  <oH  A )

Proof of Theorem atcv0
StepHypRef Expression
1 ela 23847 . 2  |-  ( A  e. HAtoms 
<->  ( A  e.  CH  /\  0H  <oH  A ) )
21simprbi 452 1  |-  ( A  e. HAtoms  ->  0H  <oH  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1726   class class class wbr 4215   CHcch 22437   0Hc0h 22443    <oH ccv 22472  HAtomscat 22473
This theorem is referenced by:  atcveq0  23856  atcv0eq  23887
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-at 23846
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