Theorem atcv0 10264

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 10261	. 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 960   class class class wbr 2624  CHcch 8793  0Hc0h 8799  Atomscat 8828   <o ccv 8829

This theorem is referenced by:  atcveq0 10270  atcv0eq 10301

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-rab 1655  df-v 1815  df-un 2053  df-sn 2416  df-pr 2417  df-op 2420  df-br 2625  df-at 10260

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