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Theorem reldmmpl 18699
Description: The multivariate polynomial constructor is a proper binary operator. (Contributed by Mario Carneiro, 21-Mar-2015.)
Assertion
Ref Expression
reldmmpl  |-  Rel  dom mPoly

Proof of Theorem reldmmpl
Dummy variables  f 
i  r  s are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-mpl 18630 . 2  |- mPoly  =  ( i  e.  _V , 
r  e.  _V  |->  [_ ( i mPwSer  r )  /  s ]_ (
ss 
{ f  e.  (
Base `  s )  |  f finSupp  ( 0g `  r ) } ) )
21reldmmpt2 6433 1  |-  Rel  dom mPoly
Colors of variables: wff setvar class
Syntax hints:   {crab 2752   _Vcvv 3056   [_csb 3374   class class class wbr 4415   dom cdm 4852   Rel wrel 4857   ` cfv 5600  (class class class)co 6314   finSupp cfsupp 7908   Basecbs 15169   ↾s cress 15170   0gc0g 15386   mPwSer cmps 18623   mPoly cmpl 18625
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-9 1906  ax-10 1925  ax-11 1930  ax-12 1943  ax-13 2101  ax-ext 2441  ax-sep 4538  ax-nul 4547  ax-pr 4652
This theorem depends on definitions:  df-bi 190  df-or 376  df-an 377  df-3an 993  df-tru 1457  df-ex 1674  df-nf 1678  df-sb 1808  df-eu 2313  df-mo 2314  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2591  df-ne 2634  df-ral 2753  df-rex 2754  df-rab 2757  df-v 3058  df-dif 3418  df-un 3420  df-in 3422  df-ss 3429  df-nul 3743  df-if 3893  df-sn 3980  df-pr 3982  df-op 3986  df-br 4416  df-opab 4475  df-xp 4858  df-rel 4859  df-dm 4862  df-oprab 6318  df-mpt2 6319  df-mpl 18630
This theorem is referenced by:  mplval  18700  mplrcl  18761  mplbaspropd  18878  ply1ascl  18899  mdegfval  23059  mdegcl  23066
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