Colors of
variables: wff set class |
Syntax hints: wi 4
wa 104
wceq 1353
wcel 2148
wrex 2456
class class class wbr 4004 (class class class)co 5875
cr 7810
cc0 7811
# cap 8538 cdiv 8629 cn 8919 cz 9253 cq 9619 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709
ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4122 ax-pow 4175 ax-pr 4210 ax-un 4434 ax-setind 4537 ax-cnex 7902 ax-resscn 7903 ax-1cn 7904 ax-1re 7905 ax-icn 7906 ax-addcl 7907 ax-addrcl 7908 ax-mulcl 7909 ax-mulrcl 7910 ax-addcom 7911 ax-mulcom 7912 ax-addass 7913 ax-mulass 7914 ax-distr 7915 ax-i2m1 7916 ax-0lt1 7917 ax-1rid 7918 ax-0id 7919 ax-rnegex 7920 ax-precex 7921 ax-cnre 7922 ax-pre-ltirr 7923 ax-pre-ltwlin 7924 ax-pre-lttrn 7925 ax-pre-apti 7926 ax-pre-ltadd 7927 ax-pre-mulgt0 7928 ax-pre-mulext 7929 |
This theorem depends on definitions:
df-bi 117 df-3or 979 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-ral 2460 df-rex 2461 df-reu 2462 df-rmo 2463 df-rab 2464 df-v 2740 df-sbc 2964 df-csb 3059 df-dif 3132 df-un 3134 df-in 3136 df-ss 3143 df-pw 3578 df-sn 3599 df-pr 3600 df-op 3602 df-uni 3811 df-int 3846 df-iun 3889 df-br 4005 df-opab 4066 df-mpt 4067 df-id 4294 df-po 4297 df-iso 4298 df-xp 4633 df-rel 4634 df-cnv 4635 df-co 4636 df-dm 4637 df-rn 4638 df-res 4639 df-ima 4640 df-iota 5179 df-fun 5219 df-fn 5220 df-f 5221 df-fv 5225 df-riota 5831 df-ov 5878 df-oprab 5879 df-mpo 5880 df-1st 6141 df-2nd 6142 df-pnf 7994 df-mnf 7995 df-xr 7996 df-ltxr 7997 df-le 7998 df-sub 8130 df-neg 8131 df-reap 8532 df-ap 8539 df-div 8630 df-inn 8920 df-z 9254 df-q 9620 |
This theorem is referenced by: qssre
9630 qltlen
9640 qlttri2
9641 irradd
9646 irrmul
9647 qletric
10244 qlelttric
10245 qltnle
10246 qdceq
10247 qbtwnz
10252 qbtwnxr
10258 qavgle
10259 ioo0
10260 ioom
10261 ico0
10262 ioc0
10263 flqcl
10273 flqlelt
10276 qfraclt1
10280 qfracge0
10281 flqge
10282 flqltnz
10287 flqwordi
10288 flqbi
10290 flqbi2
10291 flqaddz
10297 flqmulnn0
10299 flltdivnn0lt
10304 ceilqval
10306 ceiqge
10309 ceiqm1l
10311 ceiqle
10313 flqleceil
10317 flqeqceilz
10318 intfracq
10320 flqdiv
10321 modqval
10324 modq0
10329 mulqmod0
10330 negqmod0
10331 modqge0
10332 modqlt
10333 modqelico
10334 modqdiffl
10335 modqmulnn
10342 modqid
10349 modqid0
10350 modqabs
10357 modqabs2
10358 modqcyc
10359 mulqaddmodid
10364 modqmuladdim
10367 modqmuladdnn0
10368 modqltm1p1mod
10376 q2txmodxeq0
10384 q2submod
10385 modqdi
10392 modqsubdir
10393 qsqeqor
10631 fimaxq
10807 qabsor
11084 qdenre
11211 expcnvre
11511 flodddiv4t2lthalf
11942 sqrt2irraplemnn
12179 sqrt2irrap
12180 qnumgt0
12198 4sqlem6
12381 blssps
13930 blss
13931 qtopbas
14025 logbgcd1irraplemap
14390 qdencn
14778 apdifflemf
14797 |