Theorem bj-vecssmodel 38310

Description: Vector spaces are modules (elemental version). This is a shorter proof of lveclmod 21388. (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 38309	. 2 ⊢ LVec ⊆ LMod
2	1	sseli 3905	1 ⊢ (𝐴 ∈ LVec → 𝐴 ∈ LMod)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2144  LModclmod 21142  LVecclvec 21384

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-ss 3897  df-lvec 21385

This theorem is used by:  bj-isrvec2  38328