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| Mirrors > Home > MPE Home > Th. List > 2t2e4 | Structured version Visualization version GIF version | ||
| Description: 2 times 2 equals 4. (Contributed by NM, 1-Aug-1999.) |
| Ref | Expression |
|---|---|
| 2t2e4 | ⊢ (2 · 2) = 4 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 2cn 12341 | . . 3 ⊢ 2 ∈ ℂ | |
| 2 | 1 | 2timesi 12404 | . 2 ⊢ (2 · 2) = (2 + 2) |
| 3 | 2p2e4 12401 | . 2 ⊢ (2 + 2) = 4 | |
| 4 | 2, 3 | eqtri 2765 | 1 ⊢ (2 · 2) = 4 |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 (class class class)co 7431 + caddc 11158 · cmul 11160 2c2 12321 4c4 12323 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 ax-resscn 11212 ax-1cn 11213 ax-icn 11214 ax-addcl 11215 ax-mulcl 11217 ax-mulcom 11219 ax-addass 11220 ax-mulass 11221 ax-distr 11222 ax-1rid 11225 ax-cnre 11228 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-rex 3071 df-rab 3437 df-v 3482 df-dif 3954 df-un 3956 df-ss 3968 df-nul 4334 df-if 4526 df-sn 4627 df-pr 4629 df-op 4633 df-uni 4908 df-br 5144 df-iota 6514 df-fv 6569 df-ov 7434 df-2 12329 df-3 12330 df-4 12331 |
| This theorem is referenced by: 4d2e2 12436 halfpm6th 12487 div4p1lem1div2 12521 3halfnz 12697 decbin0 12873 fldiv4lem1div2uz2 13876 sq2 14236 sq4e2t8 14238 discr 14279 sqoddm1div8 14282 faclbnd2 14330 4bc2eq6 14368 amgm2 15408 bpoly3 16094 sin4lt0 16231 z4even 16409 flodddiv4 16452 flodddiv4t2lthalf 16455 4nprm 16732 2exp4 17122 2exp16 17128 5prm 17146 631prm 17164 1259lem1 17168 1259lem4 17171 2503lem1 17174 2503lem2 17175 2503lem3 17176 4001lem1 17178 4001lem2 17179 4001lem3 17180 4001prm 17182 pcoass 25057 minveclem2 25460 uniioombllem5 25622 uniioombl 25624 dveflem 26017 pilem2 26496 sinhalfpilem 26505 sincosq1lem 26539 tangtx 26547 sincos4thpi 26555 heron 26881 quad2 26882 dquartlem1 26894 dquart 26896 quart1 26899 atan1 26971 log2ublem3 26991 log2ub 26992 chtub 27256 bclbnd 27324 bpos1 27327 bposlem2 27329 bposlem6 27333 bposlem9 27336 gausslemma2dlem3 27412 m1lgs 27432 2lgslem1a2 27434 2lgslem3a 27440 2lgslem3b 27441 2lgslem3c 27442 2lgslem3d 27443 pntibndlem2 27635 pntlemg 27642 pntlemr 27646 ex-fl 30466 minvecolem2 30894 polid2i 31176 quad3d 32754 quad3 35675 420lcm8e840 42012 3exp7 42054 3lexlogpow5ineq1 42055 3lexlogpow2ineq2 42060 3lexlogpow5ineq5 42061 aks4d1p1p2 42071 aks4d1p1 42077 2ap1caineq 42146 cxpi11d 42379 flt4lem 42655 3cubeslem3l 42697 3cubeslem3r 42698 wallispi2lem1 46086 wallispi2lem2 46087 stirlinglem3 46091 stirlinglem10 46098 ceil5half3 47342 fmtnorec4 47536 2exp340mod341 47720 8exp8mod9 47723 2ltceilhalf 48015 ackval2012 48612 |
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