![]() |
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 19868 | . 2 ⊢ LVec = {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} | |
2 | ssrab2 4007 | . 2 ⊢ {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} ⊆ LMod | |
3 | 1, 2 | eqsstri 3949 | 1 ⊢ LVec ⊆ LMod |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2111 {crab 3110 ⊆ wss 3881 ‘cfv 6324 Scalarcsca 16560 DivRingcdr 19495 LModclmod 19627 LVecclvec 19867 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1541 df-ex 1782 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-rab 3115 df-v 3443 df-in 3888 df-ss 3898 df-lvec 19868 |
This theorem is referenced by: bj-vecssmodel 34697 |
Copyright terms: Public domain | W3C validator |