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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 19103 | . 2 ⊢ LVec = {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} | |
2 | ssrab2 3687 | . 2 ⊢ {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} ⊆ LMod | |
3 | 1, 2 | eqsstri 3635 | 1 ⊢ LVec ⊆ LMod |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1990 {crab 2916 ⊆ wss 3574 ‘cfv 5888 Scalarcsca 15944 DivRingcdr 18747 LModclmod 18863 LVecclvec 19102 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-in 3581 df-ss 3588 df-lvec 19103 |
This theorem is referenced by: bj-vecssmodel 33144 bj-rrvecsscmn 33152 |
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