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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 11095 | . . 3 ⊢ 3 ∈ ℂ | |
2 | 1 | times2i 11148 | . 2 ⊢ (3 · 2) = (3 + 3) |
3 | 3p3e6 11161 | . 2 ⊢ (3 + 3) = 6 | |
4 | 2, 3 | eqtri 2644 | 1 ⊢ (3 · 2) = 6 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 (class class class)co 6650 + caddc 9939 · cmul 9941 2c2 11070 3c3 11071 6c6 11074 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-resscn 9993 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-addrcl 9997 ax-mulcl 9998 ax-mulrcl 9999 ax-mulcom 10000 ax-addass 10001 ax-mulass 10002 ax-distr 10003 ax-i2m1 10004 ax-1ne0 10005 ax-1rid 10006 ax-rrecex 10008 ax-cnre 10009 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-ov 6653 df-2 11079 df-3 11080 df-4 11081 df-5 11082 df-6 11083 |
This theorem is referenced by: 3t3e9 11180 8th4div3 11252 halfpm6th 11253 halfthird 11685 fac3 13067 bpoly3 14789 bpoly4 14790 sin01bnd 14915 3lcm2e6woprm 15328 3lcm2e6 15440 prmo3 15745 2exp6 15795 6nprm 15816 7prm 15817 17prm 15824 37prm 15828 83prm 15830 163prm 15832 317prm 15833 631prm 15834 1259lem3 15840 1259lem4 15841 1259lem5 15842 2503lem2 15845 4001lem1 15848 4001lem3 15850 4001prm 15852 sincos6thpi 24267 quart1 24583 log2ublem2 24674 log2ublem3 24675 log2ub 24676 basellem5 24811 basellem8 24814 cht3 24899 ppiublem1 24927 ppiub 24929 bclbnd 25005 bpos1 25008 bposlem8 25016 bposlem9 25017 2lgslem3d 25124 2lgsoddprmlem3d 25138 hgt750lem2 30730 problem4 31562 problem5 31563 pigt3 33402 lhe4.4ex1a 38528 stoweidlem13 40230 257prm 41473 127prm 41515 mod42tp1mod8 41519 6even 41620 2t6m3t4e0 42126 zlmodzxzequa 42285 |
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