Theorem atcv0 5740

Description: An atom covers the zero subspace.

Assertion

Ref	Expression
atcv0	⊢ (A ∈ Atoms → 0ℋ ⋖ A)

Proof of Theorem atcv0

Step	Hyp	Ref	Expression
1		elat 5738	. 2 ⊢ (A ∈ Atoms ↔ (A ∈ Cℋ ∧ 0ℋ ⋖ A))
2	1	pm3.27bd 263	1 ⊢ (A ∈ Atoms → 0ℋ ⋖ A)

Syntax hints:   → wi 2   ∈ wcel 1092   class class class wbr 2054   C_ℋ cch 4968  0_ℋc0h 4974  Atomscat 4980   ⋖ ccv 4981

This theorem is referenced by:  atcveq0 5746  atcv0eq 5767

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-rab 1208  df-v 1349  df-un 1490  df-sn 1811  df-pr 1812  df-op 1815  df-br 2063  df-at 5737

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