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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 19358 | . 2 ⊢ mPoly = (𝑖 ∈ V, 𝑟 ∈ V ↦ ⦋(𝑖 mPwSer 𝑟) / 𝑠⦌(𝑠 ↾s {𝑓 ∈ (Base‘𝑠) ∣ 𝑓 finSupp (0g‘𝑟)})) | |
2 | 1 | reldmmpt2 6771 | 1 ⊢ Rel dom mPoly |
Colors of variables: wff setvar class |
Syntax hints: {crab 2916 Vcvv 3200 ⦋csb 3533 class class class wbr 4653 dom cdm 5114 Rel wrel 5119 ‘cfv 5888 (class class class)co 6650 finSupp cfsupp 8275 Basecbs 15857 ↾s cress 15858 0gc0g 16100 mPwSer cmps 19351 mPoly cmpl 19353 |
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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-xp 5120 df-rel 5121 df-dm 5124 df-oprab 6654 df-mpt2 6655 df-mpl 19358 |
This theorem is referenced by: mplval 19428 mplrcl 19490 mplbaspropd 19607 ply1ascl 19628 mdegfval 23822 mdegcl 23829 |
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