Theorem bj-vecssmodel 37283

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

Step	Hyp	Ref	Expression
1		bj-vecssmod 37282	. 2 ⊢ LVec ⊆ LMod
2	1	sseli 3979	1 ⊢ (𝐴 ∈ LVec → 𝐴 ∈ LMod)

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