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Theorem bj-vecssmodel 37225
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.)
Assertion
Ref Expression
bj-vecssmodel (𝐴 ∈ LVec → 𝐴 ∈ LMod)

Proof of Theorem bj-vecssmodel
StepHypRef Expression
1 bj-vecssmod 37224 . 2 LVec ⊆ LMod
21sseli 3991 1 (𝐴 ∈ LVec → 𝐴 ∈ LMod)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2104  LModclmod 20857  LVecclvec 21101
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1963  ax-7 2003  ax-8 2106  ax-9 2114  ax-ext 2704
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1775  df-sb 2061  df-clab 2711  df-cleq 2725  df-clel 2812  df-rab 3433  df-ss 3980  df-lvec 21102
This theorem is referenced by:  bj-isrvec2  37243
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