Theorem bj-vecssmod 37346

Description: Vector spaces are modules. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-vecssmod	⊢ LVec ⊆ LMod

Proof of Theorem bj-vecssmod

Step	Hyp	Ref	Expression
1		df-lvec 21039	. 2 ⊢ LVec = {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing}
2		ssrab2 4029	. 2 ⊢ {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} ⊆ LMod
3	1, 2	eqsstri 3977	1 ⊢ LVec ⊆ LMod

Syntax hints:   ∈ wcel 2113  {crab 3396   ⊆ wss 3898  ‘cfv 6486  Scalarcsca 17166  DivRingcdr 20646  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-vecssmodel  37347