Theorem bj-vecssmodel 34558

Description: Vector spaces are modules (elemental version). This is a shorter proof of lveclmod 19872. (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 34557	. 2 ⊢ LVec ⊆ LMod
2	1	sseli 3962	1 ⊢ (𝐴 ∈ LVec → 𝐴 ∈ LMod)

Syntax hints:   → wi 4   ∈ wcel 2110  LModclmod 19628  LVecclvec 19868

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2157  ax-12 2173  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1536  df-ex 1777  df-nf 1781  df-sb 2066  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-rab 3147  df-in 3942  df-ss 3951  df-lvec 19869

This theorem is referenced by:  bj-isrvec2  34575