| Colors of
variables: wff set class |
Syntax hints:  wi 4
 wb 105  wcel 2160 class class class wbr 4018
 cr 7829
 cc0 7830
 cle 8012
 cneg 8148 |
| 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 615 ax-in2 616 ax-io 710
ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4189 ax-pr 4224 ax-un 4448 ax-setind 4551 ax-cnex 7921 ax-resscn 7922 ax-1cn 7923 ax-1re 7924 ax-icn 7925 ax-addcl 7926 ax-addrcl 7927 ax-mulcl 7928 ax-addcom 7930 ax-addass 7932 ax-distr 7934 ax-i2m1 7935 ax-0id 7938 ax-rnegex 7939 ax-cnre 7941 ax-pre-ltadd 7946 |
| This theorem depends on definitions:
df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-nel 2456 df-ral 2473 df-rex 2474 df-reu 2475 df-rab 2477 df-v 2754 df-sbc 2978 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-id 4308 df-xp 4647 df-rel 4648 df-cnv 4649 df-co 4650 df-dm 4651 df-iota 5193 df-fun 5233 df-fv 5239 df-riota 5847 df-ov 5894 df-oprab 5895 df-mpo 5896 df-pnf 8013 df-mnf 8014 df-xr 8015 df-ltxr 8016 df-le 8017 df-sub 8149 df-neg 8150 |
| This theorem is referenced by: 0mnnnnn0
9227 qsqeqor
10650 nn0abscl
11113 abslt
11116 absle
11117 dvdslelemd
11868 znnen
12423 lgsneg
14828 |
