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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-vecssmodel | Structured version Visualization version GIF version | ||
| Description: Vector spaces are modules (elemental version). This is a shorter proof of lveclmod 21105. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.) |
| Ref | Expression |
|---|---|
| bj-vecssmodel | ⊢ (𝐴 ∈ LVec → 𝐴 ∈ LMod) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bj-vecssmod 37282 | . 2 ⊢ LVec ⊆ LMod | |
| 2 | 1 | sseli 3979 | 1 ⊢ (𝐴 ∈ LVec → 𝐴 ∈ LMod) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∈ wcel 2108 LModclmod 20858 LVecclvec 21101 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-rab 3437 df-ss 3968 df-lvec 21102 |
| This theorem is referenced by: bj-isrvec2 37301 |
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