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Theorem reldmmpl 16172
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 16100 . 2  |- mPoly  =  ( i  e.  _V , 
r  e.  _V  |->  [_ ( i mPwSer  r )  /  s ]_ (
ss 
{ f  e.  (
Base `  s )  |  ( `' f
" ( _V  \  { ( 0g `  r ) } ) )  e.  Fin }
) )
21reldmmpt2 5955 1  |-  Rel  dom mPoly
Colors of variables: wff set class
Syntax hints:    e. wcel 1684   {crab 2547   _Vcvv 2788   [_csb 3081    \ cdif 3149   {csn 3640   `'ccnv 4688   dom cdm 4689   "cima 4692   Rel wrel 4694   ` cfv 5255  (class class class)co 5858   Fincfn 6863   Basecbs 13148   ↾s cress 13149   0gc0g 13400   mPwSer cmps 16087   mPoly cmpl 16089
This theorem is referenced by:  mplval  16173  mplrcl  16231  mplbaspropd  16314  ply1ascl  16335  mdegfval  19448  mdegcl  19455
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-xp 4695  df-rel 4696  df-dm 4699  df-oprab 5862  df-mpt2 5863  df-mpl 16100
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