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Theorem reldmmpl 17500
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 17425 . 2  |- mPoly  =  ( i  e.  _V , 
r  e.  _V  |->  [_ ( i mPwSer  r )  /  s ]_ (
ss 
{ f  e.  (
Base `  s )  |  f finSupp  ( 0g `  r ) } ) )
21reldmmpt2 6201 1  |-  Rel  dom mPoly
Colors of variables: wff setvar class
Syntax hints:   {crab 2719   _Vcvv 2972   [_csb 3288   class class class wbr 4292   dom cdm 4840   Rel wrel 4845   ` cfv 5418  (class class class)co 6091   finSupp cfsupp 7620   Basecbs 14174   ↾s cress 14175   0gc0g 14378   mPwSer cmps 17418   mPoly cmpl 17420
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-9 1760  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423  ax-sep 4413  ax-nul 4421  ax-pr 4531
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-eu 2257  df-mo 2258  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-ral 2720  df-rex 2721  df-rab 2724  df-v 2974  df-dif 3331  df-un 3333  df-in 3335  df-ss 3342  df-nul 3638  df-if 3792  df-sn 3878  df-pr 3880  df-op 3884  df-br 4293  df-opab 4351  df-xp 4846  df-rel 4847  df-dm 4850  df-oprab 6095  df-mpt2 6096  df-mpl 17425
This theorem is referenced by:  mplval  17501  mplrcl  17571  mplbaspropd  17691  ply1ascl  17712  mdegfval  21531  mdegcl  21540
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