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| Mirrors > Home > MPE Home > Th. List > 4t2e8 | Structured version Visualization version GIF version | ||
| Description: 4 times 2 equals 8. (Contributed by NM, 2-Aug-2004.) |
| Ref | Expression |
|---|---|
| 4t2e8 | ⊢ (4 · 2) = 8 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 4cn 12351 | . . 3 ⊢ 4 ∈ ℂ | |
| 2 | 1 | times2i 12405 | . 2 ⊢ (4 · 2) = (4 + 4) |
| 3 | 4p4e8 12421 | . 2 ⊢ (4 + 4) = 8 | |
| 4 | 2, 3 | eqtri 2765 | 1 ⊢ (4 · 2) = 8 |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 (class class class)co 7431 + caddc 11158 · cmul 11160 2c2 12321 4c4 12323 8c8 12327 |
| 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 df-7 12334 df-8 12335 |
| This theorem is referenced by: 8th4div3 12486 4t3e12 12831 sq4e2t8 14238 cu2 14239 sqoddm1div8 14282 cos2bnd 16224 2exp7 17125 2exp8 17126 8nprm 17149 19prm 17155 139prm 17161 1259lem2 17169 1259lem3 17170 1259lem4 17171 1259lem5 17172 2503lem1 17174 2503lem2 17175 4001lem1 17178 4001lem2 17179 4001lem3 17180 4001lem4 17181 quart1lem 26898 quart1 26899 quartlem1 26900 log2tlbnd 26988 log2ub 26992 bpos1 27327 bposlem8 27335 lgsdir2lem2 27370 2lgslem3a 27440 2lgslem3b 27441 2lgslem3c 27442 2lgslem3d 27443 2lgsoddprmlem2 27453 2lgsoddprmlem3c 27456 2lgsoddprmlem3d 27457 chebbnd1lem2 27514 chebbnd1lem3 27515 pntlemr 27646 ex-exp 30469 420gcd8e4 42007 420lcm8e840 42012 lcmineqlem23 42052 3lexlogpow2ineq2 42060 sum9cubes 42682 fmtno4prmfac 47559 139prmALT 47583 mod42tp1mod8 47589 3exp4mod41 47603 41prothprm 47606 8even 47700 2exp340mod341 47720 8exp8mod9 47723 |
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