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| Mirrors > Home > MPE Home > Th. List > 2t1e2 | Structured version Visualization version GIF version | ||
| Description: 2 times 1 equals 2. (Contributed by David A. Wheeler, 6-Dec-2018.) |
| Ref | Expression |
|---|---|
| 2t1e2 | ⊢ (2 · 1) = 2 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 2cn 12341 | . 2 ⊢ 2 ∈ ℂ | |
| 2 | 1 | mulridi 11265 | 1 ⊢ (2 · 1) = 2 |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 (class class class)co 7431 1c1 11156 · cmul 11160 2c2 12321 |
| 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-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 |
| This theorem is referenced by: decbin2 12874 expubnd 14217 01sqrexlem7 15287 trirecip 15899 bpoly3 16094 fsumcube 16096 ege2le3 16126 cos2tsin 16215 cos2bnd 16224 odd2np1 16378 opoe 16400 flodddiv4 16452 2mulprm 16730 pythagtriplem4 16857 2503lem2 17175 2503lem3 17176 4001lem4 17181 4001prm 17182 htpycc 25012 pco1 25048 pcohtpylem 25052 pcopt 25055 pcorevlem 25059 ovolunlem1a 25531 cos2pi 26518 coskpi 26565 dcubic2 26887 dcubic 26889 basellem3 27126 chtublem 27255 bcp1ctr 27323 bclbnd 27324 bposlem1 27328 bposlem2 27329 bposlem5 27332 2lgslem3d1 27447 2sqreultlem 27491 2sqreunnltlem 27494 chebbnd1lem1 27513 chebbnd1lem3 27515 chebbnd1 27516 frgrregord013 30414 ex-ind-dvds 30480 wrdt2ind 32938 knoppndvlem12 36524 heiborlem6 37823 3lexlogpow5ineq1 42055 aks4d1p1 42077 2np3bcnp1 42145 2ap1caineq 42146 flt4lem7 42669 jm2.23 43008 sumnnodd 45645 wallispilem4 46083 wallispi2lem1 46086 wallispi2lem2 46087 wallispi2 46088 stirlinglem11 46099 dirkertrigeqlem1 46113 fouriersw 46246 fmtnorec4 47536 lighneallem2 47593 lighneallem3 47594 3exp4mod41 47603 opoeALTV 47670 fppr2odd 47718 8exp8mod9 47723 ackval2 48603 ackval2012 48612 |
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