Theorem bj-rrvecssvec 33150

Description: Real vector spaces are vector spaces. (Contributed by BJ, 9-Jun-2019.)

Assertion

Ref	Expression
bj-rrvecssvec	⊢ ℝ-Vec ⊆ LVec

Proof of Theorem bj-rrvecssvec

Step	Hyp	Ref	Expression
1		df-bj-rrvec 33149	. 2 ⊢ ℝ-Vec = {𝑥 ∈ LVec ∣ (Scalar‘𝑥) = ℝfld}
2		ssrab2 3687	. 2 ⊢ {𝑥 ∈ LVec ∣ (Scalar‘𝑥) = ℝfld} ⊆ LVec
3	1, 2	eqsstri 3635	1 ⊢ ℝ-Vec ⊆ LVec

Syntax hints:   = wceq 1483  {crab 2916   ⊆ wss 3574  ‘cfv 5888  Scalarcsca 15944  LVecclvec 19102  ℝ_fldcrefld 19950  ℝ-Veccrrvec 33148

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rab 2921  df-in 3581  df-ss 3588  df-bj-rrvec 33149

This theorem is referenced by:  bj-rrvecssvecel  33151  bj-rrvecsscmn  33152