Theorem bj-vecssmodel 33144

Description: Vector spaces are modules (elemental version). This is a shorter proof of lveclmod 19106. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-vecssmodel	⊢ (𝐴 ∈ LVec → 𝐴 ∈ LMod)

Proof of Theorem bj-vecssmodel

Step	Hyp	Ref	Expression
1		bj-vecssmod 33143	. 2 ⊢ LVec ⊆ LMod
2	1	sseli 3599	1 ⊢ (𝐴 ∈ LVec → 𝐴 ∈ LMod)

Syntax hints:   → wi 4   ∈ wcel 1990  LModclmod 18863  LVecclvec 19102

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-lvec 19103

This theorem is referenced by: (None)