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Mirrors > Home > MPE Home > Th. List > 6t2e12 | Structured version Visualization version GIF version |
Description: 6 times 2 equals 12. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
6t2e12 | ⊢ (6 · 2) = ;12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 6cn 11452 | . . 3 ⊢ 6 ∈ ℂ | |
2 | 1 | times2i 11504 | . 2 ⊢ (6 · 2) = (6 + 6) |
3 | 6p6e12 11904 | . 2 ⊢ (6 + 6) = ;12 | |
4 | 2, 3 | eqtri 2849 | 1 ⊢ (6 · 2) = ;12 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1656 (class class class)co 6910 1c1 10260 + caddc 10262 · cmul 10264 2c2 11413 6c6 11417 ;cdc 11828 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1894 ax-4 1908 ax-5 2009 ax-6 2075 ax-7 2112 ax-8 2166 ax-9 2173 ax-10 2192 ax-11 2207 ax-12 2220 ax-13 2389 ax-ext 2803 ax-sep 5007 ax-nul 5015 ax-pow 5067 ax-pr 5129 ax-un 7214 ax-resscn 10316 ax-1cn 10317 ax-icn 10318 ax-addcl 10319 ax-addrcl 10320 ax-mulcl 10321 ax-mulrcl 10322 ax-mulcom 10323 ax-addass 10324 ax-mulass 10325 ax-distr 10326 ax-i2m1 10327 ax-1ne0 10328 ax-1rid 10329 ax-rnegex 10330 ax-rrecex 10331 ax-cnre 10332 ax-pre-lttri 10333 ax-pre-lttrn 10334 ax-pre-ltadd 10335 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 879 df-3or 1112 df-3an 1113 df-tru 1660 df-ex 1879 df-nf 1883 df-sb 2068 df-mo 2605 df-eu 2640 df-clab 2812 df-cleq 2818 df-clel 2821 df-nfc 2958 df-ne 3000 df-nel 3103 df-ral 3122 df-rex 3123 df-reu 3124 df-rab 3126 df-v 3416 df-sbc 3663 df-csb 3758 df-dif 3801 df-un 3803 df-in 3805 df-ss 3812 df-pss 3814 df-nul 4147 df-if 4309 df-pw 4382 df-sn 4400 df-pr 4402 df-tp 4404 df-op 4406 df-uni 4661 df-iun 4744 df-br 4876 df-opab 4938 df-mpt 4955 df-tr 4978 df-id 5252 df-eprel 5257 df-po 5265 df-so 5266 df-fr 5305 df-we 5307 df-xp 5352 df-rel 5353 df-cnv 5354 df-co 5355 df-dm 5356 df-rn 5357 df-res 5358 df-ima 5359 df-pred 5924 df-ord 5970 df-on 5971 df-lim 5972 df-suc 5973 df-iota 6090 df-fun 6129 df-fn 6130 df-f 6131 df-f1 6132 df-fo 6133 df-f1o 6134 df-fv 6135 df-ov 6913 df-om 7332 df-wrecs 7677 df-recs 7739 df-rdg 7777 df-er 8014 df-en 8229 df-dom 8230 df-sdom 8231 df-pnf 10400 df-mnf 10401 df-ltxr 10403 df-nn 11358 df-2 11421 df-3 11422 df-4 11423 df-5 11424 df-6 11425 df-7 11426 df-8 11427 df-9 11428 df-n0 11626 df-dec 11829 |
This theorem is referenced by: 6t3e18 11935 6lcm4e12 15709 2exp16 16170 139prm 16203 1259lem1 16210 1259lem4 16213 2503lem1 16216 2503lem2 16217 2503lem3 16218 4001lem1 16220 4001lem4 16223 log2ublem3 25095 fmtno4prmfac 42328 139prmALT 42355 2exp7 42358 |
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