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Mirrors > Home > MPE Home > Th. List > Mathboxes > lvecgrp | Structured version Visualization version GIF version |
Description: A vector space is a group. (Contributed by SN, 28-May-2023.) |
Ref | Expression |
---|---|
lvecgrp | ⊢ (𝑊 ∈ LVec → 𝑊 ∈ Grp) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lveclmod 20552 | . 2 ⊢ (𝑊 ∈ LVec → 𝑊 ∈ LMod) | |
2 | 1 | lmodgrpd 40682 | 1 ⊢ (𝑊 ∈ LVec → 𝑊 ∈ Grp) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2106 Grpcgrp 18740 LVecclvec 20548 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2707 ax-nul 5261 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-sb 2068 df-clab 2714 df-cleq 2728 df-clel 2814 df-ne 2942 df-ral 3063 df-rab 3406 df-v 3445 df-sbc 3738 df-dif 3911 df-un 3913 df-in 3915 df-ss 3925 df-nul 4281 df-if 4485 df-sn 4585 df-pr 4587 df-op 4591 df-uni 4864 df-br 5104 df-iota 6445 df-fv 6501 df-ov 7356 df-lmod 20309 df-lvec 20549 |
This theorem is referenced by: (None) |
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