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Theorem reldmmpl 19248
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 19179 . 2 mPoly = (𝑖 ∈ V, 𝑟 ∈ V ↦ (𝑖 mPwSer 𝑟) / 𝑠(𝑠s {𝑓 ∈ (Base‘𝑠) ∣ 𝑓 finSupp (0g𝑟)}))
21reldmmpt2 6669 1 Rel dom mPoly
Colors of variables: wff setvar class
Syntax hints:  {crab 2900  Vcvv 3173  csb 3499   class class class wbr 4583  dom cdm 5038  Rel wrel 5043  cfv 5804  (class class class)co 6549   finSupp cfsupp 8158  Basecbs 15695  s cress 15696  0gc0g 15923   mPwSer cmps 19172   mPoly cmpl 19174
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709  ax-nul 4717  ax-pr 4833
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-eu 2462  df-mo 2463  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-br 4584  df-opab 4644  df-xp 5044  df-rel 5045  df-dm 5048  df-oprab 6553  df-mpt2 6554  df-mpl 19179
This theorem is referenced by:  mplval  19249  mplrcl  19311  mplbaspropd  19428  ply1ascl  19449  mdegfval  23626  mdegcl  23633
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