Theorem reldmmdeg 23817

Description: Multivariate degree is a binary operation. (Contributed by Stefan O'Rear, 28-Mar-2015.)

Assertion

Ref	Expression
reldmmdeg	|- Rel dom mDeg

Proof of Theorem reldmmdeg

Dummy variables i r h f are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-mdeg 23815	. 2 |- mDeg = ( i e. _V , r e. _V |-> ( f e. ( Base ` ( i mPoly r ) ) |-> sup ( ran ( h e. ( f supp ( 0g ` r ) ) |-> (ℂfld gsumg h ) ) , RR* , < ) ) )
2	1	reldmmpt2 6771	1 |- Rel dom mDeg

Syntax hints:   _Vcvv 3200   |-> cmpt 4729   dom cdm 5114   ran crn 5115   Rel wrel 5119   ` cfv 5888  (class class class)co 6650   supp csupp 7295   supcsup 8346   RR*cxr 10073   < clt 10074   Basecbs 15857   0gc0g 16100   gsum_g cgsu 16101   mPoly cmpl 19353  ℂ_fldccnfld 19746   mDeg cmdg 23813

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-sep 4781  ax-nul 4789  ax-pr 4906

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-eu 2474  df-mo 2475  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rab 2921  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-if 4087  df-sn 4178  df-pr 4180  df-op 4184  df-br 4654  df-opab 4713  df-xp 5120  df-rel 5121  df-dm 5124  df-oprab 6654  df-mpt2 6655  df-mdeg 23815

This theorem is referenced by:  mdegfval  23822  deg1fval  23840