Colors of
variables: wff
setvar class |
Syntax hints:
โ wi 4 = wceq 1542
โ wcel 2107 (class class class)co 7358
โcc 11050 ยท
cmul 11057 2c2 12209
โcexp 13968 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914
ax-6 1972 ax-7 2012 ax-8 2109
ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2708 ax-sep 5257 ax-nul 5264 ax-pow 5321 ax-pr 5385 ax-un 7673 ax-cnex 11108 ax-resscn 11109 ax-1cn 11110 ax-icn 11111 ax-addcl 11112 ax-addrcl 11113 ax-mulcl 11114 ax-mulrcl 11115 ax-mulcom 11116 ax-addass 11117 ax-mulass 11118 ax-distr 11119 ax-i2m1 11120 ax-1ne0 11121 ax-1rid 11122 ax-rnegex 11123 ax-rrecex 11124 ax-cnre 11125 ax-pre-lttri 11126 ax-pre-lttrn 11127 ax-pre-ltadd 11128 ax-pre-mulgt0 11129 |
This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2539 df-eu 2568 df-clab 2715 df-cleq 2729 df-clel 2815 df-nfc 2890 df-ne 2945 df-nel 3051 df-ral 3066 df-rex 3075 df-reu 3355 df-rab 3409 df-v 3448 df-sbc 3741 df-csb 3857 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 df-pss 3930 df-nul 4284 df-if 4488 df-pw 4563 df-sn 4588 df-pr 4590 df-op 4594 df-uni 4867 df-iun 4957 df-br 5107 df-opab 5169 df-mpt 5190 df-tr 5224 df-id 5532 df-eprel 5538 df-po 5546 df-so 5547 df-fr 5589 df-we 5591 df-xp 5640 df-rel 5641 df-cnv 5642 df-co 5643 df-dm 5644 df-rn 5645 df-res 5646 df-ima 5647 df-pred 6254 df-ord 6321 df-on 6322 df-lim 6323 df-suc 6324 df-iota 6449 df-fun 6499 df-fn 6500 df-f 6501 df-f1 6502 df-fo 6503 df-f1o 6504 df-fv 6505 df-riota 7314 df-ov 7361 df-oprab 7362 df-mpo 7363 df-om 7804 df-2nd 7923 df-frecs 8213 df-wrecs 8244 df-recs 8318 df-rdg 8357 df-er 8649 df-en 8885 df-dom 8886 df-sdom 8887 df-pnf 11192 df-mnf 11193 df-xr 11194 df-ltxr 11195 df-le 11196 df-sub 11388 df-neg 11389 df-nn 12155 df-2 12217
df-n0 12415 df-z 12501
df-uz 12765 df-seq 13908 df-exp 13969 |
This theorem is referenced by: sqoddm1div8
14147 sqrtmul
15145 sqreulem
15245 bhmafibid1cn
15349 bhmafibid2cn
15350 bhmafibid1
15351 pythagtriplem1
16689 prmreclem1
16789 ipcau2
24601 csbren
24766 chordthmlem4
26188 heron
26191 quad2
26192 dquart
26206 cxp2limlem
26328 basellem8
26440 lgsdir
26683 2sqlem3
26771 2sqlem4
26772 2sqlem8
26777 2sqblem
26782 2sqmod
26787 axsegconlem9
27877 ax5seglem1
27880 ax5seglem2
27881 ax5seglem3
27883 rrndstprj2
36293 3cubeslem2
41011 3cubeslem3r
41013 pellexlem6
41160 pell1234qrne0
41179 pell1234qrreccl
41180 pell1234qrmulcl
41181 pell14qrgt0
41185 pell14qrdich
41195 rmxyneg
41247 sqrtcval
41920 wallispi2lem1
44319 stirlinglem3
44324 stirlinglem10
44331 itscnhlc0yqe
46852 itschlc0yqe
46853 itsclc0yqsollem1
46855 itsclc0xyqsolr
46862 itsclquadb
46869 2itscplem1
46871 2itscplem2
46872 itscnhlinecirc02plem1
46875 |