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Theorem ismon1p 20065
 Description: Being a monic polynomial. (Contributed by Stefan O'Rear, 28-Mar-2015.)
Hypotheses
Ref Expression
uc1pval.p Poly1
uc1pval.b
uc1pval.z
uc1pval.d deg1
mon1pval.m Monic1p
mon1pval.o
Assertion
Ref Expression
ismon1p coe1

Proof of Theorem ismon1p
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 neeq1 2609 . . . 4
2 fveq2 5728 . . . . . 6 coe1 coe1
3 fveq2 5728 . . . . . 6
42, 3fveq12d 5734 . . . . 5 coe1 coe1
54eqeq1d 2444 . . . 4 coe1 coe1
61, 5anbi12d 692 . . 3 coe1 coe1
7 uc1pval.p . . . 4 Poly1
8 uc1pval.b . . . 4
9 uc1pval.z . . . 4
10 uc1pval.d . . . 4 deg1
11 mon1pval.m . . . 4 Monic1p
12 mon1pval.o . . . 4
137, 8, 9, 10, 11, 12mon1pval 20064 . . 3 coe1
146, 13elrab2 3094 . 2 coe1
15 3anass 940 . 2 coe1 coe1
1614, 15bitr4i 244 1 coe1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   w3a 936   wceq 1652   wcel 1725   wne 2599  cfv 5454  cbs 13469  c0g 13723  cur 15662  Poly1cpl1 16571  coe1cco1 16574   deg1 cdg1 19977  Monic1pcmn1 20048 This theorem is referenced by:  mon1pcl  20067  mon1pn0  20069  mon1pldg  20072  uc1pmon1p  20074  ply1remlem  20085  mon1pid  27501  mon1psubm  27502 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 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403 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 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-iota 5418  df-fun 5456  df-fv 5462  df-slot 13473  df-base 13474  df-mon1 20053
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