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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 11706 | . . 3 ⊢ 3 ∈ ℂ | |
2 | 1 | times2i 11764 | . 2 ⊢ (3 · 2) = (3 + 3) |
3 | 3p3e6 11777 | . 2 ⊢ (3 + 3) = 6 | |
4 | 2, 3 | eqtri 2841 | 1 ⊢ (3 · 2) = 6 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 (class class class)co 7145 + caddc 10528 · cmul 10530 2c2 11680 3c3 11681 6c6 11684 |
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 df-5 11691 df-6 11692 |
This theorem is referenced by: 3t3e9 11792 8th4div3 11845 halfpm6th 11846 halfthird 12229 fac3 13628 bpoly3 15400 bpoly4 15401 sin01bnd 15526 3lcm2e6woprm 15947 3lcm2e6 16060 prmo3 16365 2exp6 16410 6nprm 16431 7prm 16432 17prm 16438 37prm 16442 83prm 16444 163prm 16446 317prm 16447 631prm 16448 1259lem3 16454 1259lem4 16455 1259lem5 16456 2503lem2 16459 4001lem1 16462 4001lem3 16464 4001prm 16466 sincos6thpi 25028 pigt3 25030 quart1 25361 log2ublem2 25452 log2ublem3 25453 log2ub 25454 basellem5 25589 basellem8 25592 cht3 25677 ppiublem1 25705 ppiub 25707 bclbnd 25783 bpos1 25786 bposlem8 25794 bposlem9 25795 2lgslem3d 25902 2lgsoddprmlem3d 25916 hgt750lem2 31822 problem4 32808 problem5 32809 3cubeslem3l 39161 3cubeslem3r 39162 lhe4.4ex1a 40538 stoweidlem13 42175 257prm 43600 127prm 43640 mod42tp1mod8 43644 6even 43753 2exp340mod341 43775 2t6m3t4e0 44324 zlmodzxzequa 44479 |
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