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Mirrors > Home > MPE Home > Th. List > reldmmdeg | Structured version Visualization version GIF version |
Description: Multivariate degree is a binary operation. (Contributed by Stefan O'Rear, 28-Mar-2015.) |
Ref | Expression |
---|---|
reldmmdeg | ⊢ Rel dom mDeg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mdeg 24643 | . 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 7279 | 1 ⊢ Rel dom mDeg |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3494 ↦ cmpt 5138 dom cdm 5549 ran crn 5550 Rel wrel 5554 ‘cfv 6349 (class class class)co 7150 supp csupp 7824 supcsup 8898 ℝ*cxr 10668 < clt 10669 Basecbs 16477 0gc0g 16707 Σg cgsu 16708 mPoly cmpl 20127 ℂfldccnfld 20539 mDeg cmdg 24641 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 ax-sep 5195 ax-nul 5202 ax-pr 5321 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-mo 2618 df-eu 2650 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-rab 3147 df-v 3496 df-dif 3938 df-un 3940 df-in 3942 df-ss 3951 df-nul 4291 df-if 4467 df-sn 4561 df-pr 4563 df-op 4567 df-br 5059 df-opab 5121 df-xp 5555 df-rel 5556 df-dm 5559 df-oprab 7154 df-mpo 7155 df-mdeg 24643 |
This theorem is referenced by: mdegfval 24650 deg1fval 24668 |
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