Theorem bj-vecssmodel 37347

Description: Vector spaces are modules (elemental version). This is a shorter proof of lveclmod 21042. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-vecssmodel	⊢ (𝐴 ∈ LVec → 𝐴 ∈ LMod)

Proof of Theorem bj-vecssmodel

Step	Hyp	Ref	Expression
1		bj-vecssmod 37346	. 2 ⊢ LVec ⊆ LMod
2	1	sseli 3926	1 ⊢ (𝐴 ∈ LVec → 𝐴 ∈ LMod)

Syntax hints:   → wi 4   ∈ wcel 2113  LModclmod 20795  LVecclvec 21038

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-rab 3397  df-ss 3915  df-lvec 21039

This theorem is referenced by:  bj-isrvec2  37365