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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 21948 | . 2 ⊢ mPoly = (𝑖 ∈ V, 𝑟 ∈ V ↦ ⦋(𝑖 mPwSer 𝑟) / 𝑠⦌(𝑠 ↾s {𝑓 ∈ (Base‘𝑠) ∣ 𝑓 finSupp (0g‘𝑟)})) | |
2 | 1 | reldmmpo 7566 | 1 ⊢ Rel dom mPoly |
Colors of variables: wff setvar class |
Syntax hints: {crab 3432 Vcvv 3477 ⦋csb 3907 class class class wbr 5147 dom cdm 5688 Rel wrel 5693 ‘cfv 6562 (class class class)co 7430 finSupp cfsupp 9398 Basecbs 17244 ↾s cress 17273 0gc0g 17485 mPwSer cmps 21941 mPoly cmpl 21943 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-10 2138 ax-11 2154 ax-12 2174 ax-ext 2705 ax-sep 5301 ax-nul 5311 ax-pr 5437 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1539 df-fal 1549 df-ex 1776 df-nf 1780 df-sb 2062 df-mo 2537 df-eu 2566 df-clab 2712 df-cleq 2726 df-clel 2813 df-nfc 2889 df-rab 3433 df-v 3479 df-dif 3965 df-un 3967 df-ss 3979 df-nul 4339 df-if 4531 df-sn 4631 df-pr 4633 df-op 4637 df-br 5148 df-opab 5210 df-xp 5694 df-rel 5695 df-dm 5698 df-oprab 7434 df-mpo 7435 df-mpl 21948 |
This theorem is referenced by: mplval 22026 mplrcl 22031 selvval 22156 ismhp 22161 psdmplcl 22183 mplbaspropd 22253 ply1ascl 22276 mdegfval 26115 |
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