Theorem bj-rrvecssvecel 33151

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

Assertion

Ref	Expression
bj-rrvecssvecel	|- ( A e. RR-Vec -> A e. LVec )

Proof of Theorem bj-rrvecssvecel

Step	Hyp	Ref	Expression
1		bj-rrvecssvec 33150	. 2 |- RR-Vec C_ LVec
2	1	sseli 3599	1 |- ( A e. RR-Vec -> A e. LVec )

Syntax hints:   -> wi 4   e. wcel 1990   LVecclvec 19102  RR-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: (None)