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Theorem reldmmdeg 21639
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  h  f are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-mdeg 21637 . 2  |- mDeg  =  ( i  e.  _V , 
r  e.  _V  |->  ( f  e.  ( Base `  ( i mPoly  r ) )  |->  sup ( ran  (
h  e.  ( f supp  ( 0g `  r
) )  |->  (fld  gsumg  h ) ) , 
RR* ,  <  ) ) )
21reldmmpt2 6298 1  |-  Rel  dom mDeg
Colors of variables: wff setvar class
Syntax hints:   _Vcvv 3065    |-> cmpt 4445   dom cdm 4935   ran crn 4936   Rel wrel 4940   ` cfv 5513  (class class class)co 6187   supp csupp 6787   supcsup 7788   RR*cxr 9515    < clt 9516   Basecbs 14273   0gc0g 14477    gsumg cgsu 14478   mPoly cmpl 17523  ℂfldccnfld 17924   mDeg cmdg 21635
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430  ax-sep 4508  ax-nul 4516  ax-pr 4626
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2264  df-mo 2265  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2599  df-ne 2644  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3067  df-dif 3426  df-un 3428  df-in 3430  df-ss 3437  df-nul 3733  df-if 3887  df-sn 3973  df-pr 3975  df-op 3979  df-br 4388  df-opab 4446  df-xp 4941  df-rel 4942  df-dm 4945  df-oprab 6191  df-mpt2 6192  df-mdeg 21637
This theorem is referenced by:  mdegfval  21644  deg1fval  21664
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