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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 20870 | . 2 ⊢ mPoly = (𝑖 ∈ V, 𝑟 ∈ V ↦ ⦋(𝑖 mPwSer 𝑟) / 𝑠⦌(𝑠 ↾s {𝑓 ∈ (Base‘𝑠) ∣ 𝑓 finSupp (0g‘𝑟)})) | |
2 | 1 | reldmmpo 7344 | 1 ⊢ Rel dom mPoly |
Colors of variables: wff setvar class |
Syntax hints: {crab 3065 Vcvv 3408 ⦋csb 3811 class class class wbr 5053 dom cdm 5551 Rel wrel 5556 ‘cfv 6380 (class class class)co 7213 finSupp cfsupp 8985 Basecbs 16760 ↾s cress 16784 0gc0g 16944 mPwSer cmps 20863 mPoly cmpl 20865 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2158 ax-12 2175 ax-ext 2708 ax-sep 5192 ax-nul 5199 ax-pr 5322 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-3an 1091 df-tru 1546 df-fal 1556 df-ex 1788 df-nf 1792 df-sb 2071 df-mo 2539 df-eu 2568 df-clab 2715 df-cleq 2729 df-clel 2816 df-nfc 2886 df-rab 3070 df-v 3410 df-dif 3869 df-un 3871 df-in 3873 df-ss 3883 df-nul 4238 df-if 4440 df-sn 4542 df-pr 4544 df-op 4548 df-br 5054 df-opab 5116 df-xp 5557 df-rel 5558 df-dm 5561 df-oprab 7217 df-mpo 7218 df-mpl 20870 |
This theorem is referenced by: mplval 20953 mplrcl 20956 mplbaspropd 21158 ply1ascl 21179 mdegfval 24960 mdegcl 24967 |
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