Theorem reldmmdeg 25807

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 25805	. 2 ⊢ mDeg = (𝑖 ∈ V, 𝑟 ∈ V ↦ (𝑓 ∈ (Base‘(𝑖 mPoly 𝑟)) ↦ sup(ran (ℎ ∈ (𝑓 supp (0g‘𝑟)) ↦ (ℂfld Σg ℎ)), ℝ*, < )))
2	1	reldmmpo 7545	1 ⊢ Rel dom mDeg

Syntax hints:  Vcvv 3472   ↦ cmpt 5230  dom cdm 5675  ran crn 5676  Rel wrel 5680  ‘cfv 6542  (class class class)co 7411   supp csupp 8148  supcsup 9437  ℝ^*cxr 11251   < clt 11252  Basecbs 17148  0_gc0g 17389   Σ_g cgsu 17390  ℂ_fldccnfld 21144   mPoly cmpl 21678   mDeg cmdg 25803

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-10 2135  ax-11 2152  ax-12 2169  ax-ext 2701  ax-sep 5298  ax-nul 5305  ax-pr 5426

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 844  df-3an 1087  df-tru 1542  df-fal 1552  df-ex 1780  df-nf 1784  df-sb 2066  df-mo 2532  df-eu 2561  df-clab 2708  df-cleq 2722  df-clel 2808  df-nfc 2883  df-rab 3431  df-v 3474  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4322  df-if 4528  df-sn 4628  df-pr 4630  df-op 4634  df-br 5148  df-opab 5210  df-xp 5681  df-rel 5682  df-dm 5685  df-oprab 7415  df-mpo 7416  df-mdeg 25805

This theorem is referenced by:  mdegfval  25815  deg1fval  25833