Colors of
variables: wff set class |
Syntax hints:
→ wi 4 ∈ wcel 2148
‘cfv 5216 ℤcz 9252 ℚcq 9618
⌊cfl 10267 |
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 4121 ax-pow 4174 ax-pr 4209 ax-un 4433 ax-setind 4536 ax-cnex 7901 ax-resscn 7902 ax-1cn 7903 ax-1re 7904 ax-icn 7905 ax-addcl 7906 ax-addrcl 7907 ax-mulcl 7908 ax-mulrcl 7909 ax-addcom 7910 ax-mulcom 7911 ax-addass 7912 ax-mulass 7913 ax-distr 7914 ax-i2m1 7915 ax-0lt1 7916 ax-1rid 7917 ax-0id 7918 ax-rnegex 7919 ax-precex 7920 ax-cnre 7921 ax-pre-ltirr 7922 ax-pre-ltwlin 7923 ax-pre-lttrn 7924 ax-pre-apti 7925 ax-pre-ltadd 7926 ax-pre-mulgt0 7927 ax-pre-mulext 7928 ax-arch 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 2739 df-sbc 2963 df-csb 3058 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-int 3845 df-iun 3888 df-br 4004 df-opab 4065 df-mpt 4066 df-id 4293 df-po 4296 df-iso 4297 df-xp 4632 df-rel 4633 df-cnv 4634 df-co 4635 df-dm 4636 df-rn 4637 df-res 4638 df-ima 4639 df-iota 5178 df-fun 5218 df-fn 5219 df-f 5220 df-fv 5224 df-riota 5830 df-ov 5877 df-oprab 5878 df-mpo 5879 df-1st 6140 df-2nd 6141 df-pnf 7993 df-mnf 7994 df-xr 7995 df-ltxr 7996 df-le 7997 df-sub 8129 df-neg 8130 df-reap 8531 df-ap 8538 df-div 8629 df-inn 8919 df-n0 9176 df-z 9253 df-q 9619
df-rp 9653 df-fl 10269 |
This theorem is referenced by: flqge
10281 flqlt
10282 flid
10283 flqltnz
10286 flqwordi
10287 flqword2
10288 flqaddz
10296 flhalf
10301 flltdivnn0lt
10303 fldiv4p1lem1div2
10304 ceiqcl
10306 ceiqge
10308 ceiqm1l
10310 intfracq
10319 flqdiv
10320 modqval
10323 modqvalr
10324 modqcl
10325 flqpmodeq
10326 modq0
10328 modqge0
10331 modqlt
10332 modqdiffl
10334 modqdifz
10335 modqmulnn
10341 modqvalp1
10342 zmodcl
10343 modqcyc
10358 modqadd1
10360 modqmuladd
10365 modqmul1
10376 modqdi
10391 modqsubdir
10392 iexpcyc
10624 facavg
10725 dvdsmod
11867 divalglemnn
11922 divalgmod
11931 flodddiv4t2lthalf
11941 modgcd
11991 hashdvds
12220 prmdiv
12234 odzdvds
12244 fldivp1
12345 pcfac
12347 pcbc
12348 mulgmodid
13020 |