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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 18924 | . 2 ⊢ LVec = {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} | |
2 | ssrab2 3650 | . 2 ⊢ {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} ⊆ LMod | |
3 | 1, 2 | eqsstri 3598 | 1 ⊢ LVec ⊆ LMod |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1977 {crab 2900 ⊆ wss 3540 ‘cfv 5804 Scalarcsca 15771 DivRingcdr 18570 LModclmod 18686 LVecclvec 18923 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-rab 2905 df-in 3547 df-ss 3554 df-lvec 18924 |
This theorem is referenced by: bj-vecssmodel 32321 bj-rrvecsscmn 32329 |
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