Theorem bj-vecssmodel 37954

Description: Vector spaces are modules (elemental version). This is a shorter proof of lveclmod 21238. (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 37953	. 2 ⊢ LVec ⊆ LMod
2	1	sseli 3932	1 ⊢ (𝐴 ∈ LVec → 𝐴 ∈ LMod)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2142  LModclmod 20992  LVecclvec 21234

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-rab 3416  df-ss 3921  df-lvec 21235

This theorem is used by:  bj-isrvec2  37972