Mathbox for BJ < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-vecssmod Structured version   Visualization version   GIF version

Theorem bj-vecssmod 33473
 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
StepHypRef Expression
1 df-lvec 19326 . 2 LVec = {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing}
2 ssrab2 3829 . 2 {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} ⊆ LMod
31, 2eqsstri 3777 1 LVec ⊆ LMod
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2140  {crab 3055   ⊆ wss 3716  ‘cfv 6050  Scalarcsca 16167  DivRingcdr 18970  LModclmod 19086  LVecclvec 19325 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1989  ax-6 2055  ax-7 2091  ax-9 2149  ax-10 2169  ax-11 2184  ax-12 2197  ax-13 2392  ax-ext 2741 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2048  df-clab 2748  df-cleq 2754  df-clel 2757  df-nfc 2892  df-rab 3060  df-in 3723  df-ss 3730  df-lvec 19326 This theorem is referenced by:  bj-vecssmodel  33474  bj-rrvecsscmn  33482
 Copyright terms: Public domain W3C validator