Colors of
variables: wff
setvar class |
Syntax hints:
โ wi 4 = wceq 1534
โ wcel 2099 (class class class)co 7420
โcc 11137 1c1 11140
+ caddc 11142 ยท
cmul 11144 โ0cn0 12503 โcexp 14059 |
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-cnex 11195 ax-resscn 11196 ax-1cn 11197 ax-icn 11198 ax-addcl 11199 ax-addrcl 11200 ax-mulcl 11201 ax-mulrcl 11202 ax-mulcom 11203 ax-addass 11204 ax-mulass 11205 ax-distr 11206 ax-i2m1 11207 ax-1ne0 11208 ax-1rid 11209 ax-rnegex 11210 ax-rrecex 11211 ax-cnre 11212 ax-pre-lttri 11213 ax-pre-lttrn 11214 ax-pre-ltadd 11215 ax-pre-mulgt0 11216 |
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-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-pss 3966 df-nul 4324 df-if 4530 df-pw 4605 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4909 df-iun 4998 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5576 df-eprel 5582 df-po 5590 df-so 5591 df-fr 5633 df-we 5635 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-pred 6305 df-ord 6372 df-on 6373 df-lim 6374 df-suc 6375 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-om 7871 df-2nd 7994 df-frecs 8287 df-wrecs 8318 df-recs 8392 df-rdg 8431 df-er 8725 df-en 8965 df-dom 8966 df-sdom 8967 df-pnf 11281 df-mnf 11282 df-xr 11283 df-ltxr 11284 df-le 11285 df-sub 11477 df-neg 11478 df-nn 12244 df-n0 12504 df-z 12590
df-uz 12854 df-seq 14000 df-exp 14060 |
This theorem is referenced by: expmordi
14164 facubnd
14292 hashmap
14427 binomlem
15808 incexclem
15815 geoserg
15845 cvgrat
15862 efcllem
16054 oexpneg
16322 pwp1fsum
16368 bitsp1
16406 bitsmod
16411 bitsinv1lem
16416 sadcaddlem
16432 sadadd2lem
16434 rplpwr
16533 eulerthlem2
16751 prmdiv
16754 vfermltlALT
16771 pcprendvds2
16810 pcpremul
16812 prmpwdvds
16873 2expltfac
17062 plyco
26188 dgrcolem1
26221 ftalem5
27022 bposlem5
27234 pntlemq
27547 pntlemr
27548 pntlemj
27549 ostth2lem2
27580 ostth2lem3
27581 rusgrnumwwlks
29798 ex-ind-dvds
30284 nexple
33628 faclimlem3
35339 faclim2
35342 nn0prpwlem
35806 3lexlogpow5ineq5
41531 nicomachus
41872 3cubeslem2
42105 3cubeslem3l
42106 3cubeslem3r
42107 mzpexpmpt
42165 pell14qrexpclnn0
42286 jm2.17a
42381 jm2.17b
42382 jm2.17c
42383 jm2.18
42409 cnsrexpcl
42589 inductionexd
43585 binomcxplemnotnn0
43793 stoweidlem3
45391 stoweidlem19
45407 stirlinglem4
45465 stirlinglem7
45468 etransclem23
45645 sqrtpwpw2p
46878 fmtnorec2lem
46882 fmtnorec4
46889 fmtnoprmfac1lem
46904 fmtnoprmfac2
46907 fmtnofac1
46910 lighneallem3
46947 oexpnegALTV
47017 fppr2odd
47071 tgoldbachlt
47156 dignn0flhalflem2
47689 dignn0ehalf
47690 nn0sumshdiglemA
47692 nn0sumshdiglemB
47693 itcovalt2lem2lem2
47747 |