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Theorem reldmmdeg 23621
 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 23619 . 2 mDeg = (𝑖 ∈ V, 𝑟 ∈ V ↦ (𝑓 ∈ (Base‘(𝑖 mPoly 𝑟)) ↦ sup(ran ( ∈ (𝑓 supp (0g𝑟)) ↦ (ℂfld Σg )), ℝ*, < )))
21reldmmpt2 6669 1 Rel dom mDeg
 Colors of variables: wff setvar class Syntax hints:  Vcvv 3173   ↦ cmpt 4643  dom cdm 5038  ran crn 5039  Rel wrel 5043  ‘cfv 5804  (class class class)co 6549   supp csupp 7182  supcsup 8229  ℝ*cxr 9952   < clt 9953  Basecbs 15695  0gc0g 15923   Σg cgsu 15924   mPoly cmpl 19174  ℂfldccnfld 19567   mDeg cmdg 23617 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709  ax-nul 4717  ax-pr 4833 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-eu 2462  df-mo 2463  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-br 4584  df-opab 4644  df-xp 5044  df-rel 5045  df-dm 5048  df-oprab 6553  df-mpt2 6554  df-mdeg 23619 This theorem is referenced by:  mdegfval  23626  deg1fval  23644
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