Theorem reldmmdeg 24643

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 24641	. 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 7277	1 ⊢ Rel dom mDeg

Syntax hints:  Vcvv 3493   ↦ cmpt 5137  dom cdm 5548  ran crn 5549  Rel wrel 5553  ‘cfv 6348  (class class class)co 7148   supp csupp 7822  supcsup 8896  ℝ^*cxr 10666   < clt 10667  Basecbs 16475  0_gc0g 16705   Σ_g cgsu 16706   mPoly cmpl 20125  ℂ_fldccnfld 20537   mDeg cmdg 24639

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1905  ax-6 1964  ax-7 2009  ax-8 2110  ax-9 2118  ax-10 2139  ax-11 2154  ax-12 2170  ax-ext 2791  ax-sep 5194  ax-nul 5201  ax-pr 5320

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1084  df-tru 1534  df-ex 1775  df-nf 1779  df-sb 2064  df-mo 2616  df-eu 2648  df-clab 2798  df-cleq 2812  df-clel 2891  df-nfc 2961  df-rab 3145  df-v 3495  df-dif 3937  df-un 3939  df-in 3941  df-ss 3950  df-nul 4290  df-if 4466  df-sn 4560  df-pr 4562  df-op 4566  df-br 5058  df-opab 5120  df-xp 5554  df-rel 5555  df-dm 5558  df-oprab 7152  df-mpo 7153  df-mdeg 24641

This theorem is referenced by:  mdegfval  24648  deg1fval  24666