Theorem bj-vecssmod 36816

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 20990	. 2 ⊢ LVec = {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing}
2		ssrab2 4069	. 2 ⊢ {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} ⊆ LMod
3	1, 2	eqsstri 4007	1 ⊢ LVec ⊆ LMod

Syntax hints:   ∈ wcel 2098  {crab 3419   ⊆ wss 3940  ‘cfv 6542  Scalarcsca 17233  DivRingcdr 20626  LModclmod 20745  LVecclvec 20989

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696

This theorem depends on definitions:  df-bi 206  df-an 395  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-rab 3420  df-ss 3957  df-lvec 20990

This theorem is referenced by:  bj-vecssmodel  36817