Colors of
variables: wff
setvar class |
Syntax hints:
= wceq 1540 โ wcel 2105
(class class class)co 7412 โcc 11114
ยท cmul 11121 2c2 12274
โcexp 14034 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912
ax-6 1970 ax-7 2010 ax-8 2107
ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2702 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7729 ax-cnex 11172 ax-resscn 11173 ax-1cn 11174 ax-icn 11175 ax-addcl 11176 ax-addrcl 11177 ax-mulcl 11178 ax-mulrcl 11179 ax-mulcom 11180 ax-addass 11181 ax-mulass 11182 ax-distr 11183 ax-i2m1 11184 ax-1ne0 11185 ax-1rid 11186 ax-rnegex 11187 ax-rrecex 11188 ax-cnre 11189 ax-pre-lttri 11190 ax-pre-lttrn 11191 ax-pre-ltadd 11192 ax-pre-mulgt0 11193 |
This theorem depends on definitions:
df-bi 206 df-an 396
df-or 845 df-3or 1087 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-nf 1785 df-sb 2067 df-mo 2533 df-eu 2562 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-ne 2940 df-nel 3046 df-ral 3061 df-rex 3070 df-reu 3376 df-rab 3432 df-v 3475 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-pss 3967 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-iun 4999 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5574 df-eprel 5580 df-po 5588 df-so 5589 df-fr 5631 df-we 5633 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 df-pred 6300 df-ord 6367 df-on 6368 df-lim 6369 df-suc 6370 df-iota 6495 df-fun 6545 df-fn 6546 df-f 6547 df-f1 6548 df-fo 6549 df-f1o 6550 df-fv 6551 df-riota 7368 df-ov 7415 df-oprab 7416 df-mpo 7417 df-om 7860 df-2nd 7980 df-frecs 8272 df-wrecs 8303 df-recs 8377 df-rdg 8416 df-er 8709 df-en 8946 df-dom 8947 df-sdom 8948 df-pnf 11257 df-mnf 11258 df-xr 11259 df-ltxr 11260 df-le 11261 df-sub 11453 df-neg 11454 df-nn 12220 df-2 12282
df-n0 12480 df-z 12566
df-uz 12830 df-seq 13974 df-exp 14035 |
This theorem is referenced by: sqrecii
14154 sqdivi
14156 sqge0i
14159 lt2sqi
14160 le2sqi
14161 sq11i
14162 sq2
14168 sq3
14169 sq4e2t8
14170 i2
14173 expnass
14179 binom2i
14183 sq10
14231 3dec
14233 nn0le2msqi
14234 nn0opthlem1
14235 nn0opth2i
14238 faclbnd4lem1
14260 sqrtmsq2i
15341 pythagtriplem12
16766 pythagtriplem14
16768 prmlem1
17048 prmlem2
17060 4001prm
17085 mcubic
26693 dquartlem1
26697 quart1lem
26701 quart1
26702 log2ublem3
26794 birthday
26800 bposlem7
27136 bposlem8
27137 bposlem9
27138 ax5seglem7
28626 normlem1
30796 nmopcoadji
31787 dpmul4
32513 hgt750lem2
34128 quad3
35119 cntotbnd
37128 3lexlogpow5ineq1
41386 3lexlogpow5ineq5
41392 sq9
41667 flt4lem5e
41861 sq45
41876 resqrtvalex
42859 imsqrtvalex
42860 fmtno5lem4
46683 flsqrt5
46721 lighneallem4a
46735 |