Colors of
variables: wff
setvar class |
Syntax hints:
โ wi 4 = wceq 1534
โ wcel 2099 (class class class)co 7420
โcc 11137 ยท
cmul 11144 2c2 12298
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-2 12306
df-n0 12504 df-z 12590
df-uz 12854 df-seq 14000 df-exp 14060 |
This theorem is referenced by: sqoddm1div8
14238 sqrtmul
15239 sqreulem
15339 bhmafibid1cn
15443 bhmafibid2cn
15444 bhmafibid1
15445 pythagtriplem1
16785 prmreclem1
16885 ipcau2
25175 csbren
25340 chordthmlem4
26780 heron
26783 quad2
26784 dquart
26798 cxp2limlem
26921 basellem8
27033 lgsdir
27278 2sqlem3
27366 2sqlem4
27367 2sqlem8
27372 2sqblem
27377 2sqmod
27382 axsegconlem9
28749 ax5seglem1
28752 ax5seglem2
28753 ax5seglem3
28755 rrndstprj2
37304 3cubeslem2
42105 3cubeslem3r
42107 pellexlem6
42254 pell1234qrne0
42273 pell1234qrreccl
42274 pell1234qrmulcl
42275 pell14qrgt0
42279 pell14qrdich
42289 rmxyneg
42341 sqrtcval
43071 wallispi2lem1
45459 stirlinglem3
45464 stirlinglem10
45471 itscnhlc0yqe
47832 itschlc0yqe
47833 itsclc0yqsollem1
47835 itsclc0xyqsolr
47842 itsclquadb
47849 2itscplem1
47851 2itscplem2
47852 itscnhlinecirc02plem1
47855 |