| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∧ w3a 1084
= wceq 1533 ∈
wcel 2098 ≠ wne 2937
‘cfv 6553 (class class class)co 7426
1oc1o 8488
ℕ0cn0 12512
Basecbs 17189 0gc0g 17430 Ringcrg 20187
mPoly cmpl 21853 Poly1cpl1 22114
deg1 cdg1 26015 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905
ax-6 1963 ax-7 2003 ax-8 2100
ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2699 ax-rep 5289 ax-sep 5303 ax-nul 5310 ax-pow 5369 ax-pr 5433 ax-un 7748 ax-cnex 11204 ax-resscn 11205 ax-1cn 11206 ax-icn 11207 ax-addcl 11208 ax-addrcl 11209 ax-mulcl 11210 ax-mulrcl 11211 ax-mulcom 11212 ax-addass 11213 ax-mulass 11214 ax-distr 11215 ax-i2m1 11216 ax-1ne0 11217 ax-1rid 11218 ax-rnegex 11219 ax-rrecex 11220 ax-cnre 11221 ax-pre-lttri 11222 ax-pre-lttrn 11223 ax-pre-ltadd 11224 ax-pre-mulgt0 11225 ax-addf 11227 |
| This theorem depends on definitions:
df-bi 206 df-an 395
df-or 846 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2529 df-eu 2558 df-clab 2706 df-cleq 2720 df-clel 2806 df-nfc 2881 df-ne 2938 df-nel 3044 df-ral 3059 df-rex 3068 df-rmo 3374 df-reu 3375 df-rab 3431 df-v 3475 df-sbc 3779 df-csb 3895 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-pss 3968 df-nul 4327 df-if 4533 df-pw 4608 df-sn 4633 df-pr 4635 df-tp 4637 df-op 4639 df-uni 4913 df-int 4954 df-iun 5002 df-br 5153 df-opab 5215 df-mpt 5236 df-tr 5270 df-id 5580 df-eprel 5586 df-po 5594 df-so 5595 df-fr 5637 df-se 5638 df-we 5639 df-xp 5688 df-rel 5689 df-cnv 5690 df-co 5691 df-dm 5692 df-rn 5693 df-res 5694 df-ima 5695 df-pred 6310 df-ord 6377 df-on 6378 df-lim 6379 df-suc 6380 df-iota 6505 df-fun 6555 df-fn 6556 df-f 6557 df-f1 6558 df-fo 6559 df-f1o 6560 df-fv 6561 df-isom 6562 df-riota 7382 df-ov 7429 df-oprab 7430 df-mpo 7431 df-of 7692 df-om 7879 df-1st 8001 df-2nd 8002 df-supp 8174 df-frecs 8295 df-wrecs 8326 df-recs 8400 df-rdg 8439 df-1o 8495 df-er 8733 df-map 8855 df-ixp 8925 df-en 8973 df-dom 8974 df-sdom 8975 df-fin 8976 df-fsupp 9396 df-sup 9475 df-oi 9543 df-card 9972 df-pnf 11290 df-mnf 11291 df-xr 11292 df-ltxr 11293 df-le 11294 df-sub 11486 df-neg 11487 df-nn 12253 df-2 12315
df-3 12316 df-4 12317
df-5 12318 df-6 12319
df-7 12320 df-8 12321
df-9 12322 df-n0 12513 df-z 12599
df-dec 12718 df-uz 12863 df-fz 13527 df-fzo 13670 df-seq 14009 df-hash 14332 df-struct 17125 df-sets 17142 df-slot 17160 df-ndx 17172 df-base 17190 df-ress 17219 df-plusg 17255 df-mulr 17256 df-starv 17257 df-sca 17258 df-vsca 17259 df-ip 17260 df-tset 17261 df-ple 17262 df-ds 17264 df-unif 17265 df-hom 17266 df-cco 17267 df-0g 17432 df-gsum 17433 df-prds 17438 df-pws 17440 df-mgm 18609 df-sgrp 18688 df-mnd 18704 df-submnd 18750 df-grp 18907 df-minusg 18908 df-subg 19092 df-cntz 19282 df-cmn 19751 df-abl 19752 df-mgp 20089 df-ur 20136 df-ring 20189 df-cring 20190 df-cnfld 21294 df-psr 21856 df-mpl 21858 df-opsr 21860 df-psr1 22117 df-ply1 22119 df-mdeg 26016 df-deg1 26017 |
| This theorem is referenced by: deg1n0ima
26053 deg1nn0clb
26054 deg1lt0
26055 deg1ldg
26056 deg1ldgdomn
26058 coe1mul4
26064 deg1add
26067 deg1scl
26077 deg1mul2
26078 ply1domn
26087 ply1divmo
26099 ply1divex
26100 uc1pdeg
26111 deg1submon1p
26116 fta1glem1
26130 fta1g
26132 drnguc1p
26136 ply1unit
33301 ply1degltel
33306 ply1degleel
33307 ig1pmindeg
33313 irngnzply1lem
33409 minplyirredlem
33421 irredminply
33425 algextdeglem7
33432 algextdeglem8
33433 deg1mul
41651 deg1gprod
41652 deg1pow
41653 mon1psubm
42676 deg1mhm
42677 |
