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Theorem reldmmdeg 24014
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 24012 . 2 mDeg = (𝑖 ∈ V, 𝑟 ∈ V ↦ (𝑓 ∈ (Base‘(𝑖 mPoly 𝑟)) ↦ sup(ran ( ∈ (𝑓 supp (0g𝑟)) ↦ (ℂfld Σg )), ℝ*, < )))
21reldmmpt2 6934 1 Rel dom mDeg
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3338  cmpt 4879  dom cdm 5264  ran crn 5265  Rel wrel 5269  cfv 6047  (class class class)co 6811   supp csupp 7461  supcsup 8509  *cxr 10263   < clt 10264  Basecbs 16057  0gc0g 16300   Σg cgsu 16301   mPoly cmpl 19553  fldccnfld 19946   mDeg cmdg 24010
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1986  ax-6 2052  ax-7 2088  ax-9 2146  ax-10 2166  ax-11 2181  ax-12 2194  ax-13 2389  ax-ext 2738  ax-sep 4931  ax-nul 4939  ax-pr 5053
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2045  df-eu 2609  df-mo 2610  df-clab 2745  df-cleq 2751  df-clel 2754  df-nfc 2889  df-rab 3057  df-v 3340  df-dif 3716  df-un 3718  df-in 3720  df-ss 3727  df-nul 4057  df-if 4229  df-sn 4320  df-pr 4322  df-op 4326  df-br 4803  df-opab 4863  df-xp 5270  df-rel 5271  df-dm 5274  df-oprab 6815  df-mpt2 6816  df-mdeg 24012
This theorem is referenced by:  mdegfval  24019  deg1fval  24037
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