Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
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 20132 | . 2 ⊢ mPoly = (𝑖 ∈ V, 𝑟 ∈ V ↦ ⦋(𝑖 mPwSer 𝑟) / 𝑠⦌(𝑠 ↾s {𝑓 ∈ (Base‘𝑠) ∣ 𝑓 finSupp (0g‘𝑟)})) | |
2 | 1 | reldmmpo 7279 | 1 ⊢ Rel dom mPoly |
Colors of variables: wff setvar class |
Syntax hints: {crab 3142 Vcvv 3495 ⦋csb 3883 class class class wbr 5059 dom cdm 5550 Rel wrel 5555 ‘cfv 6350 (class class class)co 7150 finSupp cfsupp 8827 Basecbs 16477 ↾s cress 16478 0gc0g 16707 mPwSer cmps 20125 mPoly cmpl 20127 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2156 ax-12 2172 ax-ext 2793 ax-sep 5196 ax-nul 5203 ax-pr 5322 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-mo 2618 df-eu 2650 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-rab 3147 df-v 3497 df-dif 3939 df-un 3941 df-in 3943 df-ss 3952 df-nul 4292 df-if 4468 df-sn 4562 df-pr 4564 df-op 4568 df-br 5060 df-opab 5122 df-xp 5556 df-rel 5557 df-dm 5560 df-oprab 7154 df-mpo 7155 df-mpl 20132 |
This theorem is referenced by: mplval 20202 mplrcl 20264 mplbaspropd 20399 ply1ascl 20420 mdegfval 24650 mdegcl 24657 |
Copyright terms: Public domain | W3C validator |