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Mirrors > Home > MPE Home > Th. List > ismon1p | Structured version Visualization version Unicode version |
Description: Being a monic polynomial. (Contributed by Stefan O'Rear, 28-Mar-2015.) |
Ref | Expression |
---|---|
uc1pval.p | Poly1 |
uc1pval.b | |
uc1pval.z | |
uc1pval.d | deg1 |
mon1pval.m | Monic1p |
mon1pval.o |
Ref | Expression |
---|---|
ismon1p | coe1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neeq1 2856 | . . . 4 | |
2 | fveq2 6191 | . . . . . 6 coe1 coe1 | |
3 | fveq2 6191 | . . . . . 6 | |
4 | 2, 3 | fveq12d 6197 | . . . . 5 coe1 coe1 |
5 | 4 | eqeq1d 2624 | . . . 4 coe1 coe1 |
6 | 1, 5 | anbi12d 747 | . . 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 | |
13 | 7, 8, 9, 10, 11, 12 | mon1pval 23901 | . . 3 coe1 |
14 | 6, 13 | elrab2 3366 | . 2 coe1 |
15 | 3anass 1042 | . 2 coe1 coe1 | |
16 | 14, 15 | bitr4i 267 | 1 coe1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 wne 2794 cfv 5888 cbs 15857 c0g 16100 cur 18501 Poly1cpl1 19547 coe1cco1 19548 deg1 cdg1 23814 Monic1pcmn1 23885 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-slot 15861 df-base 15863 df-mon1 23890 |
This theorem is referenced by: mon1pcl 23904 mon1pn0 23906 mon1pldg 23909 uc1pmon1p 23911 ply1remlem 23922 mon1pid 37783 mon1psubm 37784 |
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