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Theorem uc1pn0 20060
 Description: Unitic polynomials are not zero. (Contributed by Stefan O'Rear, 28-Mar-2015.)
Hypotheses
Ref Expression
uc1pn0.p Poly1
uc1pn0.z
uc1pn0.c Unic1p
Assertion
Ref Expression
uc1pn0

Proof of Theorem uc1pn0
StepHypRef Expression
1 uc1pn0.p . . 3 Poly1
2 eqid 2435 . . 3
3 uc1pn0.z . . 3
4 eqid 2435 . . 3 deg1 deg1
5 uc1pn0.c . . 3 Unic1p
6 eqid 2435 . . 3 Unit Unit
71, 2, 3, 4, 5, 6isuc1p 20055 . 2 coe1 deg1 Unit
87simp2bi 973 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725   wne 2598  cfv 5446  cbs 13461  c0g 13715  Unitcui 15736  Poly1cpl1 16563  coe1cco1 16566   deg1 cdg1 19969  Unic1pcuc1p 20041 This theorem is referenced by:  uc1pdeg  20062  q1peqb  20069 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pow 4369  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-iota 5410  df-fun 5448  df-fv 5454  df-slot 13465  df-base 13466  df-uc1p 20046
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