Theorem bj-rrvecssvecel 32328

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

Assertion

Ref	Expression
bj-rrvecssvecel	⊢ (𝐴 ∈ ℝ-Vec → 𝐴 ∈ LVec)

Proof of Theorem bj-rrvecssvecel

Step	Hyp	Ref	Expression
1		bj-rrvecssvec 32327	. 2 ⊢ ℝ-Vec ⊆ LVec
2	1	sseli 3564	1 ⊢ (𝐴 ∈ ℝ-Vec → 𝐴 ∈ LVec)

Syntax hints:   → wi 4   ∈ wcel 1977  LVecclvec 18923  ℝ-Veccrrvec 32325

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-in 3547  df-ss 3554  df-bj-rrvec 32326

This theorem is referenced by: (None)