Theorem reldmmdeg 26097

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 26095	. 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 7568	1 ⊢ Rel dom mDeg

Syntax hints:  Vcvv 3479   ↦ cmpt 5224  dom cdm 5684  ran crn 5685  Rel wrel 5689  ‘cfv 6560  (class class class)co 7432   supp csupp 8186  supcsup 9481  ℝ^*cxr 11295   < clt 11296  Basecbs 17248  0_gc0g 17485   Σ_g cgsu 17486  ℂ_fldccnfld 21365   mPoly cmpl 21927   mDeg cmdg 26093

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-10 2140  ax-11 2156  ax-12 2176  ax-ext 2707  ax-sep 5295  ax-nul 5305  ax-pr 5431

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1779  df-nf 1783  df-sb 2064  df-mo 2539  df-eu 2568  df-clab 2714  df-cleq 2728  df-clel 2815  df-nfc 2891  df-rab 3436  df-v 3481  df-dif 3953  df-un 3955  df-ss 3967  df-nul 4333  df-if 4525  df-sn 4626  df-pr 4628  df-op 4632  df-br 5143  df-opab 5205  df-xp 5690  df-rel 5691  df-dm 5694  df-oprab 7436  df-mpo 7437  df-mdeg 26095

This theorem is referenced by:  mdegfval  26102  deg1fval  26120