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Theorem reldmmdeg 22328
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 22326 . 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 6398 1  |-  Rel  dom mDeg
Colors of variables: wff setvar class
Syntax hints:   _Vcvv 3095    |-> cmpt 4495   dom cdm 4989   ran crn 4990   Rel wrel 4994   ` cfv 5578  (class class class)co 6281   supp csupp 6903   supcsup 7902   RR*cxr 9630    < clt 9631   Basecbs 14509   0gc0g 14714    gsumg cgsu 14715   mPoly cmpl 17876  ℂfldccnfld 18294   mDeg cmdg 22324
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-9 1808  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421  ax-sep 4558  ax-nul 4566  ax-pr 4676
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-eu 2272  df-mo 2273  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-br 4438  df-opab 4496  df-xp 4995  df-rel 4996  df-dm 4999  df-oprab 6285  df-mpt2 6286  df-mdeg 22326
This theorem is referenced by:  mdegfval  22333  deg1fval  22353
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