Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2099
≠ wne 2937 (class class class)co 7420
ℝcr 11137 0cc0 11138
1c1 11139 / cdiv 11901 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906
ax-6 1964 ax-7 2004 ax-8 2101
ax-9 2109 ax-10 2130 ax-11 2147 ax-12 2167 ax-ext 2699 ax-sep 5299 ax-nul 5306 ax-pow 5365 ax-pr 5429 ax-un 7740 ax-resscn 11195 ax-1cn 11196 ax-icn 11197 ax-addcl 11198 ax-addrcl 11199 ax-mulcl 11200 ax-mulrcl 11201 ax-mulcom 11202 ax-addass 11203 ax-mulass 11204 ax-distr 11205 ax-i2m1 11206 ax-1ne0 11207 ax-1rid 11208 ax-rnegex 11209 ax-rrecex 11210 ax-cnre 11211 ax-pre-lttri 11212 ax-pre-lttrn 11213 ax-pre-ltadd 11214 ax-pre-mulgt0 11215 |
This theorem depends on definitions:
df-bi 206 df-an 396
df-or 847 df-3or 1086 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2530 df-eu 2559 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 3373 df-reu 3374 df-rab 3430 df-v 3473 df-sbc 3777 df-csb 3893 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4324 df-if 4530 df-pw 4605 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4909 df-br 5149 df-opab 5211 df-mpt 5232 df-id 5576 df-po 5590 df-so 5591 df-xp 5684 df-rel 5685 df-cnv 5686 df-co 5687 df-dm 5688 df-rn 5689 df-res 5690 df-ima 5691 df-iota 6500 df-fun 6550 df-fn 6551 df-f 6552 df-f1 6553 df-fo 6554 df-f1o 6555 df-fv 6556 df-riota 7376 df-ov 7423 df-oprab 7424 df-mpo 7425 df-er 8724 df-en 8964 df-dom 8965 df-sdom 8966 df-pnf 11280 df-mnf 11281 df-xr 11282 df-ltxr 11283 df-le 11284 df-sub 11476 df-neg 11477 df-div 11902 |
This theorem is referenced by: recgt0
12090 prodgt0
12091 ltdiv1
12108 ltrec
12126 lerec
12127 lediv12a
12137 nnrecl
12500 rpnnen1lem5
12995 expnlbnd
14227 cnsubrg
21359 evth
24884 ncvs1
25084 reeff1o
26383 isosctrlem2
26750 chordthmlem2
26764 cxplim
26903 nv1
30484 nmblolbii
30608 norm1
31058 norm1exi
31059 nmbdoplbi
31833 nmcoplbi
31837 nmbdfnlbi
31858 nmcfnlbi
31861 branmfn
31914 strlem1
32059 dya2icoseg
33897 logdivsqrle
34282 rtprmirr
41906 irrapxlem2
42243 irrapxlem5
42246 pell1234qrreccl
42274 pell14qrdich
42289 radcnvrat
43751 hashnzfzclim
43759 reclt0
44773 ltdiv23neg
44776 sumnnodd
45018 ioodvbdlimc1lem2
45320 ioodvbdlimc2lem
45322 stoweidlem7
45395 stoweidlem11
45399 stoweidlem14
45402 stoweidlem25
45413 stoweidlem36
45424 stoweidlem42
45430 stirlinglem10
45471 stirlinglem11
45472 stirlinglem12
45473 fourierdlem40
45535 fourierdlem78
45572 pimrecltpos
46096 pimrecltneg
46112 eenglngeehlnmlem1
47810 |