Theorem bj-vecssmod 37648

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 21100	. 2 ⊢ LVec = {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing}
2		ssrab2 4018	. 2 ⊢ {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} ⊆ LMod
3	1, 2	eqsstri 3968	1 ⊢ LVec ⊆ LMod

Syntax hints:   ∈ wcel 2119  {crab 3392   ⊆ wss 3890  ‘cfv 6492  Scalarcsca 17221  DivRingcdr 20708  LModclmod 20857  LVecclvec 21099

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-rab 3393  df-ss 3907  df-lvec 21100

This theorem is referenced by:  bj-vecssmodel  37649