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Theorem reldmmdeg 24699
 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 24697 . 2 mDeg = (𝑖 ∈ V, 𝑟 ∈ V ↦ (𝑓 ∈ (Base‘(𝑖 mPoly 𝑟)) ↦ sup(ran ( ∈ (𝑓 supp (0g𝑟)) ↦ (ℂfld Σg )), ℝ*, < )))
21reldmmpo 7275 1 Rel dom mDeg
 Colors of variables: wff setvar class Syntax hints:  Vcvv 3442   ↦ cmpt 5114  dom cdm 5523  ran crn 5524  Rel wrel 5528  ‘cfv 6332  (class class class)co 7145   supp csupp 7826  supcsup 8906  ℝ*cxr 10681   < clt 10682  Basecbs 16495  0gc0g 16725   Σg cgsu 16726  ℂfldccnfld 20112   mPoly cmpl 20614   mDeg cmdg 24695 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770  ax-sep 5171  ax-nul 5178  ax-pr 5299 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2598  df-eu 2629  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-v 3444  df-dif 3886  df-un 3888  df-in 3890  df-ss 3900  df-nul 4247  df-if 4429  df-sn 4529  df-pr 4531  df-op 4535  df-br 5035  df-opab 5097  df-xp 5529  df-rel 5530  df-dm 5533  df-oprab 7149  df-mpo 7150  df-mdeg 24697 This theorem is referenced by:  mdegfval  24707  deg1fval  24725
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