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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 11700 | . . 3 ⊢ 2 ∈ ℂ | |
2 | 1 | 2timesi 11763 | . 2 ⊢ (2 · 2) = (2 + 2) |
3 | 2p2e4 11760 | . 2 ⊢ (2 + 2) = 4 | |
4 | 2, 3 | eqtri 2841 | 1 ⊢ (2 · 2) = 4 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 (class class class)co 7145 + caddc 10528 · cmul 10530 2c2 11680 4c4 11682 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-resscn 10582 ax-1cn 10583 ax-icn 10584 ax-addcl 10585 ax-mulcl 10587 ax-mulcom 10589 ax-addass 10590 ax-mulass 10591 ax-distr 10592 ax-1rid 10595 ax-cnre 10598 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ral 3140 df-rex 3141 df-rab 3144 df-v 3494 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-if 4464 df-sn 4558 df-pr 4560 df-op 4564 df-uni 4831 df-br 5058 df-iota 6307 df-fv 6356 df-ov 7148 df-2 11688 df-3 11689 df-4 11690 |
This theorem is referenced by: 4d2e2 11795 halfpm6th 11846 div4p1lem1div2 11880 3halfnz 12049 decbin0 12226 fldiv4lem1div2uz2 13194 sq2 13548 sq4e2t8 13550 discr 13589 sqoddm1div8 13592 faclbnd2 13639 4bc2eq6 13677 amgm2 14717 bpoly3 15400 sin4lt0 15536 z4even 15711 flodddiv4 15752 flodddiv4t2lthalf 15755 4nprm 16027 2exp4 16409 2exp16 16412 5prm 16430 631prm 16448 1259lem1 16452 1259lem4 16455 2503lem1 16458 2503lem2 16459 2503lem3 16460 4001lem1 16462 4001lem2 16463 4001lem3 16464 4001prm 16466 pcoass 23555 minveclem2 23956 uniioombllem5 24115 uniioombl 24117 dveflem 24503 pilem2 24967 sinhalfpilem 24976 sincosq1lem 25010 tangtx 25018 sincos4thpi 25026 heron 25343 quad2 25344 dquartlem1 25356 dquart 25358 quart1 25361 atan1 25433 log2ublem3 25453 log2ub 25454 chtub 25715 bclbnd 25783 bpos1 25786 bposlem2 25788 bposlem6 25792 bposlem9 25795 gausslemma2dlem3 25871 m1lgs 25891 2lgslem1a2 25893 2lgslem3a 25899 2lgslem3b 25900 2lgslem3c 25901 2lgslem3d 25902 pntibndlem2 26094 pntlemg 26101 pntlemr 26105 ex-fl 28153 minvecolem2 28579 polid2i 28861 quad3 32810 3cubeslem3l 39161 3cubeslem3r 39162 wallispi2lem1 42233 wallispi2lem2 42234 stirlinglem3 42238 stirlinglem10 42245 fmtnorec4 43588 2exp340mod341 43775 8exp8mod9 43778 |
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