Theorem bj-vecssmod 37276

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 21017	. 2 ⊢ LVec = {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing}
2		ssrab2 4046	. 2 ⊢ {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} ⊆ LMod
3	1, 2	eqsstri 3996	1 ⊢ LVec ⊆ LMod

Syntax hints:   ∈ wcel 2109  {crab 3408   ⊆ wss 3917  ‘cfv 6514  Scalarcsca 17230  DivRingcdr 20645  LModclmod 20773  LVecclvec 21016

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-rab 3409  df-ss 3934  df-lvec 21017

This theorem is referenced by:  bj-vecssmodel  37277