Colors of
variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4
↔ wb 105 ∈
wcel 2148 class class class wbr 4004
ℝcr 7810 <
clt 7992 ≤ cle 7993 |
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-14 2151 ax-ext 2159 ax-sep 4122 ax-pow 4175 ax-pr 4210 |
This theorem depends on definitions:
df-bi 117 df-3an 980 df-tru 1356 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-ral 2460 df-rex 2461 df-v 2740 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-br 4005 df-opab 4066 df-xp 4633 df-cnv 4635 df-xr 7996 df-le 7998 |
This theorem is referenced by: ltnsymd
8077 nltled
8078 lensymd
8079 leadd1
8387 lemul1
8550 leltap
8582 ap0gt0
8597 prodgt0
8809 prodge0
8811 lediv1
8826 lemuldiv
8838 lerec
8841 lt2msq
8843 le2msq
8858 squeeze0
8861 suprleubex
8911 0mnnnnn0
9208 elnn0z
9266 uzm1
9558 infregelbex
9598 fztri3or
10039 fzdisj
10052 uzdisj
10093 nn0disj
10138 fzouzdisj
10180 elfzonelfzo
10230 flqeqceilz
10318 modifeq2int
10386 modsumfzodifsn
10396 nn0leexp2
10690 expcanlem
10695 fimaxq
10807 resqrexlemoverl
11030 leabs
11083 absle
11098 maxleast
11222 minmax
11238 climge0
11333 pcfac
12348 cxple
14340 |