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Theorem reldmmdeg 24952
Description: Multivariate degree is a binary operation. (Contributed by Stefan O'Rear, 28-Mar-2015.)
Assertion
Ref Expression
reldmmdeg Rel dom mDeg

Proof of Theorem reldmmdeg
Dummy variables 𝑖 𝑟 𝑓 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-mdeg 24950 . 2 mDeg = (𝑖 ∈ V, 𝑟 ∈ V ↦ (𝑓 ∈ (Base‘(𝑖 mPoly 𝑟)) ↦ sup(ran ( ∈ (𝑓 supp (0g𝑟)) ↦ (ℂfld Σg )), ℝ*, < )))
21reldmmpo 7344 1 Rel dom mDeg
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3408  cmpt 5135  dom cdm 5551  ran crn 5552  Rel wrel 5556  cfv 6380  (class class class)co 7213   supp csupp 7903  supcsup 9056  *cxr 10866   < clt 10867  Basecbs 16760  0gc0g 16944   Σg cgsu 16945  fldccnfld 20363   mPoly cmpl 20865   mDeg cmdg 24948
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-mdeg 24950
This theorem is referenced by:  mdegfval  24960  deg1fval  24978
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