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Theorem atcv0 23356
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 23353 . 2  |-  ( A  e. HAtoms 
<->  ( A  e.  CH  /\  0H  <oH  A ) )
21simprbi 450 1  |-  ( A  e. HAtoms  ->  0H  <oH  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1715   class class class wbr 4125   CHcch 21943   0Hc0h 21949    <oH ccv 21978  HAtomscat 21979
This theorem is referenced by:  atcveq0  23362  atcv0eq  23393
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-ext 2347
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 937  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-clab 2353  df-cleq 2359  df-clel 2362  df-nfc 2491  df-rab 2637  df-v 2875  df-dif 3241  df-un 3243  df-in 3245  df-ss 3252  df-nul 3544  df-if 3655  df-sn 3735  df-pr 3736  df-op 3738  df-br 4126  df-at 23352
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