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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 11129 | . 2 ⊢ 2 ∈ ℂ | |
2 | 1 | mulid1i 10080 | 1 ⊢ (2 · 1) = 2 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1523 (class class class)co 6690 1c1 9975 · cmul 9979 2c2 11108 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1762 ax-4 1777 ax-5 1879 ax-6 1945 ax-7 1981 ax-9 2039 ax-10 2059 ax-11 2074 ax-12 2087 ax-13 2282 ax-ext 2631 ax-resscn 10031 ax-1cn 10032 ax-icn 10033 ax-addcl 10034 ax-addrcl 10035 ax-mulcl 10036 ax-mulrcl 10037 ax-mulcom 10038 ax-mulass 10040 ax-distr 10041 ax-i2m1 10042 ax-1ne0 10043 ax-1rid 10044 ax-rrecex 10046 ax-cnre 10047 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-3an 1056 df-tru 1526 df-ex 1745 df-nf 1750 df-sb 1938 df-clab 2638 df-cleq 2644 df-clel 2647 df-nfc 2782 df-ne 2824 df-ral 2946 df-rex 2947 df-rab 2950 df-v 3233 df-dif 3610 df-un 3612 df-in 3614 df-ss 3621 df-nul 3949 df-if 4120 df-sn 4211 df-pr 4213 df-op 4217 df-uni 4469 df-br 4686 df-iota 5889 df-fv 5934 df-ov 6693 df-2 11117 |
This theorem is referenced by: decbin2 11721 expubnd 12961 sqrlem7 14033 trirecip 14639 bpoly3 14833 fsumcube 14835 ege2le3 14864 cos2tsin 14953 cos2bnd 14962 odd2np1 15112 opoe 15134 flodddiv4 15184 pythagtriplem4 15571 2503lem2 15892 2503lem3 15893 4001lem4 15898 4001prm 15899 htpycc 22826 pco1 22861 pcohtpylem 22865 pcopt 22868 pcorevlem 22872 ovolunlem1a 23310 cos2pi 24273 coskpi 24317 dcubic1lem 24615 dcubic2 24616 dcubic 24618 mcubic 24619 basellem3 24854 chtublem 24981 bcp1ctr 25049 bclbnd 25050 bposlem1 25054 bposlem2 25055 bposlem5 25058 2lgslem3d1 25173 chebbnd1lem1 25203 chebbnd1lem3 25205 chebbnd1 25206 frgrregord013 27382 ex-ind-dvds 27448 knoppndvlem12 32639 heiborlem6 33745 jm2.23 37880 sumnnodd 40180 wallispilem4 40603 wallispi2lem1 40606 wallispi2lem2 40607 wallispi2 40608 stirlinglem11 40619 dirkertrigeqlem1 40633 fouriersw 40766 fmtnorec4 41786 lighneallem2 41848 lighneallem3 41849 3exp4mod41 41858 opoeALTV 41919 |
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