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Theorem reldmmpl 21475
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 21392 . 2 mPoly = (𝑖 ∈ V, 𝑟 ∈ V ↦ (𝑖 mPwSer 𝑟) / 𝑠(𝑠s {𝑓 ∈ (Base‘𝑠) ∣ 𝑓 finSupp (0g𝑟)}))
21reldmmpo 7525 1 Rel dom mPoly
Colors of variables: wff setvar class
Syntax hints:  {crab 3431  Vcvv 3472  csb 3888   class class class wbr 5140  dom cdm 5668  Rel wrel 5673  cfv 6531  (class class class)co 7392   finSupp cfsupp 9343  Basecbs 17125  s cress 17154  0gc0g 17366   mPwSer cmps 21385   mPoly cmpl 21387
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2702  ax-sep 5291  ax-nul 5298  ax-pr 5419
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-nf 1786  df-sb 2068  df-mo 2533  df-eu 2562  df-clab 2709  df-cleq 2723  df-clel 2809  df-nfc 2884  df-rab 3432  df-v 3474  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4522  df-sn 4622  df-pr 4624  df-op 4628  df-br 5141  df-opab 5203  df-xp 5674  df-rel 5675  df-dm 5678  df-oprab 7396  df-mpo 7397  df-mpl 21392
This theorem is referenced by:  mplval  21476  mplrcl  21479  mplbaspropd  21687  ply1ascl  21708  mdegfval  25506  mdegcl  25513
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