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Mirrors > Home > HSE Home > Th. List > atcv0 | Structured version Visualization version GIF version |
Description: An atom covers the zero subspace. (Contributed by NM, 26-Jun-2004.) (New usage is discouraged.) |
Ref | Expression |
---|---|
atcv0 | ⊢ (𝐴 ∈ HAtoms → 0ℋ ⋖ℋ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ela 29774 | . 2 ⊢ (𝐴 ∈ HAtoms ↔ (𝐴 ∈ Cℋ ∧ 0ℋ ⋖ℋ 𝐴)) | |
2 | 1 | simprbi 492 | 1 ⊢ (𝐴 ∈ HAtoms → 0ℋ ⋖ℋ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2107 class class class wbr 4888 Cℋ cch 28362 0ℋc0h 28368 ⋖ℋ ccv 28397 HAtomscat 28398 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2055 ax-9 2116 ax-10 2135 ax-11 2150 ax-12 2163 ax-13 2334 ax-ext 2754 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 837 df-3an 1073 df-tru 1605 df-ex 1824 df-nf 1828 df-sb 2012 df-clab 2764 df-cleq 2770 df-clel 2774 df-nfc 2921 df-rab 3099 df-v 3400 df-dif 3795 df-un 3797 df-in 3799 df-ss 3806 df-nul 4142 df-if 4308 df-sn 4399 df-pr 4401 df-op 4405 df-br 4889 df-at 29773 |
This theorem is referenced by: atcveq0 29783 atcv0eq 29814 |
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