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Theorem reldmmdeg 24223
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 24221 . 2 mDeg = (𝑖 ∈ V, 𝑟 ∈ V ↦ (𝑓 ∈ (Base‘(𝑖 mPoly 𝑟)) ↦ sup(ran ( ∈ (𝑓 supp (0g𝑟)) ↦ (ℂfld Σg )), ℝ*, < )))
21reldmmpt2 7036 1 Rel dom mDeg
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3414  cmpt 4954  dom cdm 5346  ran crn 5347  Rel wrel 5351  cfv 6127  (class class class)co 6910   supp csupp 7564  supcsup 8621  *cxr 10397   < clt 10398  Basecbs 16229  0gc0g 16460   Σg cgsu 16461   mPoly cmpl 19721  fldccnfld 20113   mDeg cmdg 24219
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-13 2389  ax-ext 2803  ax-sep 5007  ax-nul 5015  ax-pr 5129
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-3an 1113  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-mo 2605  df-eu 2640  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-rab 3126  df-v 3416  df-dif 3801  df-un 3803  df-in 3805  df-ss 3812  df-nul 4147  df-if 4309  df-sn 4400  df-pr 4402  df-op 4406  df-br 4876  df-opab 4938  df-xp 5352  df-rel 5353  df-dm 5356  df-oprab 6914  df-mpt2 6915  df-mdeg 24221
This theorem is referenced by:  mdegfval  24228  deg1fval  24246
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