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Theorem reldmmdeg 22187
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 22185 . 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 6395 1  |-  Rel  dom mDeg
Colors of variables: wff setvar class
Syntax hints:   _Vcvv 3113    |-> cmpt 4505   dom cdm 4999   ran crn 5000   Rel wrel 5004   ` cfv 5586  (class class class)co 6282   supp csupp 6898   supcsup 7896   RR*cxr 9623    < clt 9624   Basecbs 14483   0gc0g 14688    gsumg cgsu 14689   mPoly cmpl 17770  ℂfldccnfld 18188   mDeg cmdg 22183
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-br 4448  df-opab 4506  df-xp 5005  df-rel 5006  df-dm 5009  df-oprab 6286  df-mpt2 6287  df-mdeg 22185
This theorem is referenced by:  mdegfval  22192  deg1fval  22212
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