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Theorem reldmmdeg 19840
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 19838 . 2  |- mDeg  =  ( i  e.  _V , 
r  e.  _V  |->  ( f  e.  ( Base `  ( i mPoly  r ) )  |->  sup ( ran  (
h  e.  ( `' f " ( _V 
\  { ( 0g
`  r ) } ) )  |->  (fld  gsumg  h ) ) , 
RR* ,  <  ) ) )
21reldmmpt2 6113 1  |-  Rel  dom mDeg
Colors of variables: wff set class
Syntax hints:   _Vcvv 2892    \ cdif 3253   {csn 3750    e. cmpt 4200   `'ccnv 4810   dom cdm 4811   ran crn 4812   "cima 4814   Rel wrel 4816   ` cfv 5387  (class class class)co 6013   supcsup 7373   RR*cxr 9045    < clt 9046   Basecbs 13389   0gc0g 13643    gsumg cgsu 13644   mPoly cmpl 16328  ℂfldccnfld 16619   mDeg cmdg 19836
This theorem is referenced by:  mdegfval  19845  deg1fval  19863
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361  ax-sep 4264  ax-nul 4272  ax-pr 4337
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2235  df-mo 2236  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ne 2545  df-ral 2647  df-rex 2648  df-rab 2651  df-v 2894  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-if 3676  df-sn 3756  df-pr 3757  df-op 3759  df-br 4147  df-opab 4201  df-xp 4817  df-rel 4818  df-dm 4821  df-oprab 6017  df-mpt2 6018  df-mdeg 19838
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