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Mirrors > Home > MPE Home > Th. List > sq2 | Structured version Visualization version GIF version |
Description: The square of 2 is 4. (Contributed by NM, 22-Aug-1999.) |
Ref | Expression |
---|---|
sq2 | ⊢ (2↑2) = 4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2cn 12320 | . . 3 ⊢ 2 ∈ ℂ | |
2 | 1 | sqvali 14179 | . 2 ⊢ (2↑2) = (2 · 2) |
3 | 2t2e4 12409 | . 2 ⊢ (2 · 2) = 4 | |
4 | 2, 3 | eqtri 2753 | 1 ⊢ (2↑2) = 4 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 (class class class)co 7419 · cmul 11145 2c2 12300 4c4 12302 ↑cexp 14062 |
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 2166 ax-ext 2696 ax-sep 5300 ax-nul 5307 ax-pow 5365 ax-pr 5429 ax-un 7741 ax-cnex 11196 ax-resscn 11197 ax-1cn 11198 ax-icn 11199 ax-addcl 11200 ax-addrcl 11201 ax-mulcl 11202 ax-mulrcl 11203 ax-mulcom 11204 ax-addass 11205 ax-mulass 11206 ax-distr 11207 ax-i2m1 11208 ax-1ne0 11209 ax-1rid 11210 ax-rnegex 11211 ax-rrecex 11212 ax-cnre 11213 ax-pre-lttri 11214 ax-pre-lttrn 11215 ax-pre-ltadd 11216 ax-pre-mulgt0 11217 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 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 2703 df-cleq 2717 df-clel 2802 df-nfc 2877 df-ne 2930 df-nel 3036 df-ral 3051 df-rex 3060 df-reu 3364 df-rab 3419 df-v 3463 df-sbc 3774 df-csb 3890 df-dif 3947 df-un 3949 df-in 3951 df-ss 3961 df-pss 3964 df-nul 4323 df-if 4531 df-pw 4606 df-sn 4631 df-pr 4633 df-op 4637 df-uni 4910 df-iun 4999 df-br 5150 df-opab 5212 df-mpt 5233 df-tr 5267 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 6307 df-ord 6374 df-on 6375 df-lim 6376 df-suc 6377 df-iota 6501 df-fun 6551 df-fn 6552 df-f 6553 df-f1 6554 df-fo 6555 df-f1o 6556 df-fv 6557 df-riota 7375 df-ov 7422 df-oprab 7423 df-mpo 7424 df-om 7872 df-2nd 7995 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 11282 df-mnf 11283 df-xr 11284 df-ltxr 11285 df-le 11286 df-sub 11478 df-neg 11479 df-nn 12246 df-2 12308 df-3 12309 df-4 12310 df-n0 12506 df-z 12592 df-uz 12856 df-seq 14003 df-exp 14063 |
This theorem is referenced by: sq4e2t8 14198 cu2 14199 sqoddm1div8 14241 faclbnd2 14286 sqrt4 15255 amgm2 15352 ef01bndlem 16164 cos2bnd 16168 pythagtriplem1 16788 4sqlem12 16928 2exp4 17057 2exp5 17058 efmnd2hash 18854 lt6abl 19862 csbren 25371 minveclem2 25398 sincos6thpi 26495 heron 26815 quad2 26816 dcubic2 26821 mcubic 26824 dquartlem2 26829 dquart 26830 quart1 26833 quartlem1 26834 chtublem 27189 chtub 27190 bclbnd 27258 bposlem6 27267 bposlem8 27269 addsqnreup 27421 addsq2nreurex 27422 chebbnd1lem3 27449 chebbnd1 27450 ipidsq 30592 minvecolem2 30757 normpar2i 31038 sqsscirc1 33640 lcmineqlem21 41652 aks4d1p1p7 41677 aks4d1p1p5 41678 flt4lem5e 42215 wallispi2lem1 45597 stirlinglem3 45602 stirlinglem10 45609 fmtno1 47018 fmtno2 47027 fmtnofac1 47047 m2prm 47068 lighneallem2 47083 lighneallem4a 47085 exple2lt6 47614 ackval3 47942 ackval42 47955 ackval42a 47956 itsclc0yqsollem1 48021 itscnhlinecirc02plem1 48041 |
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