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Theorem reldmmpl 20701
 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 20619 . 2 mPoly = (𝑖 ∈ V, 𝑟 ∈ V ↦ (𝑖 mPwSer 𝑟) / 𝑠(𝑠s {𝑓 ∈ (Base‘𝑠) ∣ 𝑓 finSupp (0g𝑟)}))
21reldmmpo 7275 1 Rel dom mPoly
 Colors of variables: wff setvar class Syntax hints:  {crab 3110  Vcvv 3442  ⦋csb 3830   class class class wbr 5034  dom cdm 5523  Rel wrel 5528  ‘cfv 6332  (class class class)co 7145   finSupp cfsupp 8835  Basecbs 16495   ↾s cress 16496  0gc0g 16725   mPwSer cmps 20612   mPoly cmpl 20614 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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770  ax-sep 5171  ax-nul 5178  ax-pr 5299 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2598  df-eu 2629  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-v 3444  df-dif 3886  df-un 3888  df-in 3890  df-ss 3900  df-nul 4247  df-if 4429  df-sn 4529  df-pr 4531  df-op 4535  df-br 5035  df-opab 5097  df-xp 5529  df-rel 5530  df-dm 5533  df-oprab 7149  df-mpo 7150  df-mpl 20619 This theorem is referenced by:  mplval  20702  mplrcl  20705  mplbaspropd  20907  ply1ascl  20928  mdegfval  24707  mdegcl  24714
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