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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 19877 | . 2 ⊢ LVec = {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} | |
2 | ssrab2 4058 | . 2 ⊢ {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} ⊆ LMod | |
3 | 1, 2 | eqsstri 4003 | 1 ⊢ LVec ⊆ LMod |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2114 {crab 3144 ⊆ wss 3938 ‘cfv 6357 Scalarcsca 16570 DivRingcdr 19504 LModclmod 19636 LVecclvec 19876 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-rab 3149 df-in 3945 df-ss 3954 df-lvec 19877 |
This theorem is referenced by: bj-vecssmodel 34566 |
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