Colors of
variables: wff
setvar class |
Syntax hints:
โ wi 4 = wceq 1533
โ wcel 2098 (class class class)co 7404
โcc 11107 ยท
cmul 11114 2c2 12268
โcexp 14030 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905
ax-6 1963 ax-7 2003 ax-8 2100
ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2163 ax-ext 2697 ax-sep 5292 ax-nul 5299 ax-pow 5356 ax-pr 5420 ax-un 7721 ax-cnex 11165 ax-resscn 11166 ax-1cn 11167 ax-icn 11168 ax-addcl 11169 ax-addrcl 11170 ax-mulcl 11171 ax-mulrcl 11172 ax-mulcom 11173 ax-addass 11174 ax-mulass 11175 ax-distr 11176 ax-i2m1 11177 ax-1ne0 11178 ax-1rid 11179 ax-rnegex 11180 ax-rrecex 11181 ax-cnre 11182 ax-pre-lttri 11183 ax-pre-lttrn 11184 ax-pre-ltadd 11185 ax-pre-mulgt0 11186 |
This theorem depends on definitions:
df-bi 206 df-an 396
df-or 845 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2704 df-cleq 2718 df-clel 2804 df-nfc 2879 df-ne 2935 df-nel 3041 df-ral 3056 df-rex 3065 df-reu 3371 df-rab 3427 df-v 3470 df-sbc 3773 df-csb 3889 df-dif 3946 df-un 3948 df-in 3950 df-ss 3960 df-pss 3962 df-nul 4318 df-if 4524 df-pw 4599 df-sn 4624 df-pr 4626 df-op 4630 df-uni 4903 df-iun 4992 df-br 5142 df-opab 5204 df-mpt 5225 df-tr 5259 df-id 5567 df-eprel 5573 df-po 5581 df-so 5582 df-fr 5624 df-we 5626 df-xp 5675 df-rel 5676 df-cnv 5677 df-co 5678 df-dm 5679 df-rn 5680 df-res 5681 df-ima 5682 df-pred 6293 df-ord 6360 df-on 6361 df-lim 6362 df-suc 6363 df-iota 6488 df-fun 6538 df-fn 6539 df-f 6540 df-f1 6541 df-fo 6542 df-f1o 6543 df-fv 6544 df-riota 7360 df-ov 7407 df-oprab 7408 df-mpo 7409 df-om 7852 df-2nd 7972 df-frecs 8264 df-wrecs 8295 df-recs 8369 df-rdg 8408 df-er 8702 df-en 8939 df-dom 8940 df-sdom 8941 df-pnf 11251 df-mnf 11252 df-xr 11253 df-ltxr 11254 df-le 11255 df-sub 11447 df-neg 11448 df-nn 12214 df-2 12276
df-n0 12474 df-z 12560
df-uz 12824 df-seq 13970 df-exp 14031 |
This theorem is referenced by: sqoddm1div8
14209 sqrtmul
15210 sqreulem
15310 bhmafibid1cn
15414 bhmafibid2cn
15415 bhmafibid1
15416 pythagtriplem1
16756 prmreclem1
16856 ipcau2
25113 csbren
25278 chordthmlem4
26718 heron
26721 quad2
26722 dquart
26736 cxp2limlem
26859 basellem8
26971 lgsdir
27216 2sqlem3
27304 2sqlem4
27305 2sqlem8
27310 2sqblem
27315 2sqmod
27320 axsegconlem9
28687 ax5seglem1
28690 ax5seglem2
28691 ax5seglem3
28693 rrndstprj2
37210 3cubeslem2
41982 3cubeslem3r
41984 pellexlem6
42131 pell1234qrne0
42150 pell1234qrreccl
42151 pell1234qrmulcl
42152 pell14qrgt0
42156 pell14qrdich
42166 rmxyneg
42218 sqrtcval
42949 wallispi2lem1
45340 stirlinglem3
45345 stirlinglem10
45352 itscnhlc0yqe
47701 itschlc0yqe
47702 itsclc0yqsollem1
47704 itsclc0xyqsolr
47711 itsclquadb
47718 2itscplem1
47720 2itscplem2
47721 itscnhlinecirc02plem1
47724 |