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| Mirrors > Home > MPE Home > Th. List > 3t2e6 | Structured version Visualization version GIF version | ||
| Description: 3 times 2 equals 6. (Contributed by NM, 2-Aug-2004.) |
| Ref | Expression |
|---|---|
| 3t2e6 | ⊢ (3 · 2) = 6 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3cn 12347 | . . 3 ⊢ 3 ∈ ℂ | |
| 2 | 1 | times2i 12405 | . 2 ⊢ (3 · 2) = (3 + 3) |
| 3 | 3p3e6 12418 | . 2 ⊢ (3 + 3) = 6 | |
| 4 | 2, 3 | eqtri 2765 | 1 ⊢ (3 · 2) = 6 |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 (class class class)co 7431 + caddc 11158 · cmul 11160 2c2 12321 3c3 12322 6c6 12325 |
| 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 df-5 12332 df-6 12333 |
| This theorem is referenced by: 3t3e9 12433 8th4div3 12486 halfpm6th 12487 halfthird 12876 fac3 14319 bpoly3 16094 bpoly4 16095 sin01bnd 16221 3lcm2e6woprm 16652 3lcm2e6 16769 prmo3 17079 2exp6 17124 6nprm 17147 7prm 17148 17prm 17154 37prm 17158 83prm 17160 163prm 17162 317prm 17163 631prm 17164 1259lem3 17170 1259lem4 17171 1259lem5 17172 2503lem2 17175 4001lem1 17178 4001lem3 17180 4001prm 17182 sincos6thpi 26558 pigt3 26560 quart1 26899 log2ublem2 26990 log2ublem3 26991 log2ub 26992 basellem5 27128 basellem8 27131 cht3 27216 ppiublem1 27246 ppiub 27248 bclbnd 27324 bpos1 27327 bposlem8 27335 bposlem9 27336 2lgslem3d 27443 2lgsoddprmlem3d 27457 hgt750lem2 34667 problem4 35673 problem5 35674 3exp7 42054 3cubeslem3l 42697 3cubeslem3r 42698 lhe4.4ex1a 44348 stoweidlem13 46028 ceil5half3 47342 minusmodnep2tmod 47355 257prm 47548 127prm 47586 mod42tp1mod8 47589 6even 47698 2exp340mod341 47720 2t6m3t4e0 48264 zlmodzxzequa 48413 |
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