![]() |
Mathbox for BJ |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-vecssmod | Structured version Visualization version GIF version |
Description: Vector spaces are modules. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-vecssmod | ⊢ LVec ⊆ LMod |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-lvec 20702 | . 2 ⊢ LVec = {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} | |
2 | ssrab2 4076 | . 2 ⊢ {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} ⊆ LMod | |
3 | 1, 2 | eqsstri 4015 | 1 ⊢ LVec ⊆ LMod |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2107 {crab 3433 ⊆ wss 3947 ‘cfv 6540 Scalarcsca 17196 DivRingcdr 20304 LModclmod 20459 LVecclvec 20701 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-rab 3434 df-v 3477 df-in 3954 df-ss 3964 df-lvec 20702 |
This theorem is referenced by: bj-vecssmodel 36101 |
Copyright terms: Public domain | W3C validator |