Colors of
variables: wff
setvar class |
Syntax hints:
โ wi 4 โง wa 397
= wceq 1542 โ
wcel 2107 โ wnel 3046
class class class wbr 5109 โcfv 6500
(class class class)co 7361 โcr 11058
0cc0 11059 ici 11061
ยท cmul 11064 โค
cle 11198 2c2 12216
โ+crp 12923
โcexp 13976 โcre 14991 โcsqrt 15127 |
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 2704 ax-sep 5260 ax-nul 5267 ax-pow 5324 ax-pr 5388 ax-un 7676 ax-cnex 11115 ax-resscn 11116 ax-1cn 11117 ax-icn 11118 ax-addcl 11119 ax-addrcl 11120 ax-mulcl 11121 ax-mulrcl 11122 ax-mulcom 11123 ax-addass 11124 ax-mulass 11125 ax-distr 11126 ax-i2m1 11127 ax-1ne0 11128 ax-1rid 11129 ax-rnegex 11130 ax-rrecex 11131 ax-cnre 11132 ax-pre-lttri 11133 ax-pre-lttrn 11134 ax-pre-ltadd 11135 ax-pre-mulgt0 11136 ax-pre-sup 11137 |
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 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2941 df-nel 3047 df-ral 3062 df-rex 3071 df-rmo 3352 df-reu 3353 df-rab 3407 df-v 3449 df-sbc 3744 df-csb 3860 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-pss 3933 df-nul 4287 df-if 4491 df-pw 4566 df-sn 4591 df-pr 4593 df-op 4597 df-uni 4870 df-iun 4960 df-br 5110 df-opab 5172 df-mpt 5193 df-tr 5227 df-id 5535 df-eprel 5541 df-po 5549 df-so 5550 df-fr 5592 df-we 5594 df-xp 5643 df-rel 5644 df-cnv 5645 df-co 5646 df-dm 5647 df-rn 5648 df-res 5649 df-ima 5650 df-pred 6257 df-ord 6324 df-on 6325 df-lim 6326 df-suc 6327 df-iota 6452 df-fun 6502 df-fn 6503 df-f 6504 df-f1 6505 df-fo 6506 df-f1o 6507 df-fv 6508 df-riota 7317 df-ov 7364 df-oprab 7365 df-mpo 7366 df-om 7807 df-2nd 7926 df-frecs 8216 df-wrecs 8247 df-recs 8321 df-rdg 8360 df-er 8654 df-en 8890 df-dom 8891 df-sdom 8892 df-sup 9386 df-pnf 11199 df-mnf 11200 df-xr 11201 df-ltxr 11202 df-le 11203 df-sub 11395 df-neg 11396 df-div 11821 df-nn 12162 df-2 12224
df-3 12225 df-n0 12422 df-z 12508
df-uz 12772 df-rp 12924 df-seq 13916 df-exp 13977 df-cj 14993 df-re 14994 df-im 14995 df-sqrt 15129 |
This theorem is referenced by: remsqsqrt
15150 sqrtgt0
15152 sqrtmul
15153 sqrtle
15154 sqrt11
15156 sqrtneglem
15160 sqrtsq2
15162 absvalsq
15174 sqreulem
15253 sqsqrti
15269 pythagtriplem12
16706 pythagtriplem14
16708 pythagtriplem16
16710 trirn
24787 rrxdstprj1
24796 tan4thpi
25894 bposlem6
26660 bposlem7
26661 dchrisum0
26891 pntlemb
26968 pntlemh
26970 pntlemr
26973 axsegconlem9
27923 ax5seglem3
27929 minvecolem5
29872 rrndstprj1
36339 rrndstprj2
36340 stirlinglem3
44407 sqrtpwpw2p
45820 ehl2eudis0lt
46902 itsclc0xyqsolr
46945 |