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| Mirrors > Home > MPE Home > Th. List > reldmmpl | Structured version Visualization version GIF version | ||
| Description: The multivariate polynomial constructor is a proper binary operator. (Contributed by Mario Carneiro, 21-Mar-2015.) |
| Ref | Expression |
|---|---|
| reldmmpl | ⊢ Rel dom mPoly |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-mpl 21931 | . 2 ⊢ mPoly = (𝑖 ∈ V, 𝑟 ∈ V ↦ ⦋(𝑖 mPwSer 𝑟) / 𝑠⦌(𝑠 ↾s {𝑓 ∈ (Base‘𝑠) ∣ 𝑓 finSupp (0g‘𝑟)})) | |
| 2 | 1 | reldmmpo 7567 | 1 ⊢ Rel dom mPoly |
| Colors of variables: wff setvar class |
| Syntax hints: {crab 3436 Vcvv 3480 ⦋csb 3899 class class class wbr 5143 dom cdm 5685 Rel wrel 5690 ‘cfv 6561 (class class class)co 7431 finSupp cfsupp 9401 Basecbs 17247 ↾s cress 17274 0gc0g 17484 mPwSer cmps 21924 mPoly cmpl 21926 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-11 2157 ax-12 2177 ax-ext 2708 ax-sep 5296 ax-nul 5306 ax-pr 5432 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-nf 1784 df-sb 2065 df-mo 2540 df-eu 2569 df-clab 2715 df-cleq 2729 df-clel 2816 df-nfc 2892 df-rab 3437 df-v 3482 df-dif 3954 df-un 3956 df-ss 3968 df-nul 4334 df-if 4526 df-sn 4627 df-pr 4629 df-op 4633 df-br 5144 df-opab 5206 df-xp 5691 df-rel 5692 df-dm 5695 df-oprab 7435 df-mpo 7436 df-mpl 21931 |
| This theorem is referenced by: mplval 22009 mplrcl 22014 selvval 22139 ismhp 22144 psdmplcl 22166 mplbaspropd 22238 ply1ascl 22261 mdegfval 26101 |
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