Theorem reldmmdeg 25962

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 25960	. 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 7523	1 ⊢ Rel dom mDeg

Syntax hints:  Vcvv 3447   ↦ cmpt 5188  dom cdm 5638  ran crn 5639  Rel wrel 5643  ‘cfv 6511  (class class class)co 7387   supp csupp 8139  supcsup 9391  ℝ^*cxr 11207   < clt 11208  Basecbs 17179  0_gc0g 17402   Σ_g cgsu 17403  ℂ_fldccnfld 21264   mPoly cmpl 21815   mDeg cmdg 25958

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 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-10 2142  ax-11 2158  ax-12 2178  ax-ext 2701  ax-sep 5251  ax-nul 5261  ax-pr 5387

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2066  df-mo 2533  df-eu 2562  df-clab 2708  df-cleq 2721  df-clel 2803  df-nfc 2878  df-rab 3406  df-v 3449  df-dif 3917  df-un 3919  df-ss 3931  df-nul 4297  df-if 4489  df-sn 4590  df-pr 4592  df-op 4596  df-br 5108  df-opab 5170  df-xp 5644  df-rel 5645  df-dm 5648  df-oprab 7391  df-mpo 7392  df-mdeg 25960

This theorem is referenced by:  mdegfval  25967  deg1fval  25985