Theorem atcv0 10260

Description: An atom covers the zero subspace.

Assertion

Ref	Expression
atcv0	|- (A e. Atoms -> 0H <o A)

Proof of Theorem atcv0

Step	Hyp	Ref	Expression
1		elat 10257	. 2 |- (A e. Atoms <-> (A e. CH /\ 0H <o A))
2	1	pm3.27bi 326	1 |- (A e. Atoms -> 0H <o A)

Syntax hints:   -> wi 3   e. wcel 957   class class class wbr 2616  CHcch 8782  0Hc0h 8788  Atomscat 8817   <o ccv 8818

This theorem is referenced by:  atcveq0 10266  atcv0eq 10297

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 980  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-rab 1651  df-v 1810  df-un 2048  df-sn 2410  df-pr 2411  df-op 2414  df-br 2617  df-at 10256

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