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Theorem reldmmpl 16411
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 16339 . 2  |- mPoly  =  ( i  e.  _V , 
r  e.  _V  |->  [_ ( i mPwSer  r )  /  s ]_ (
ss 
{ f  e.  (
Base `  s )  |  ( `' f
" ( _V  \  { ( 0g `  r ) } ) )  e.  Fin }
) )
21reldmmpt2 6113 1  |-  Rel  dom mPoly
Colors of variables: wff set class
Syntax hints:    e. wcel 1717   {crab 2646   _Vcvv 2892   [_csb 3187    \ cdif 3253   {csn 3750   `'ccnv 4810   dom cdm 4811   "cima 4814   Rel wrel 4816   ` cfv 5387  (class class class)co 6013   Fincfn 7038   Basecbs 13389   ↾s cress 13390   0gc0g 13643   mPwSer cmps 16326   mPoly cmpl 16328
This theorem is referenced by:  mplval  16412  mplrcl  16470  mplbaspropd  16550  ply1ascl  16571  mdegfval  19845  mdegcl  19852
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361  ax-sep 4264  ax-nul 4272  ax-pr 4337
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2235  df-mo 2236  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ne 2545  df-ral 2647  df-rex 2648  df-rab 2651  df-v 2894  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-if 3676  df-sn 3756  df-pr 3757  df-op 3759  df-br 4147  df-opab 4201  df-xp 4817  df-rel 4818  df-dm 4821  df-oprab 6017  df-mpt2 6018  df-mpl 16339
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