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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 11700 | . 2 ⊢ 2 ∈ ℂ | |
2 | 1 | mulid1i 10633 | 1 ⊢ (2 · 1) = 2 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 (class class class)co 7145 1c1 10526 · cmul 10530 2c2 11680 |
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-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 |
This theorem is referenced by: decbin2 12227 expubnd 13529 sqrlem7 14596 trirecip 15206 bpoly3 15400 fsumcube 15402 ege2le3 15431 cos2tsin 15520 cos2bnd 15529 odd2np1 15678 opoe 15700 flodddiv4 15752 2mulprm 16025 pythagtriplem4 16144 2503lem2 16459 2503lem3 16460 4001lem4 16465 4001prm 16466 htpycc 23511 pco1 23546 pcohtpylem 23550 pcopt 23553 pcorevlem 23557 ovolunlem1a 24024 cos2pi 24989 coskpi 25035 dcubic2 25349 dcubic 25351 basellem3 25587 chtublem 25714 bcp1ctr 25782 bclbnd 25783 bposlem1 25787 bposlem2 25788 bposlem5 25791 2lgslem3d1 25906 2sqreultlem 25950 2sqreunnltlem 25953 chebbnd1lem1 25972 chebbnd1lem3 25974 chebbnd1 25975 frgrregord013 28101 ex-ind-dvds 28167 wrdt2ind 30554 knoppndvlem12 33759 heiborlem6 34975 jm2.23 39471 sumnnodd 41787 wallispilem4 42230 wallispi2lem1 42233 wallispi2lem2 42234 wallispi2 42235 stirlinglem11 42246 dirkertrigeqlem1 42260 fouriersw 42393 fmtnorec4 43588 lighneallem2 43648 lighneallem3 43649 3exp4mod41 43658 opoeALTV 43725 fppr2odd 43773 8exp8mod9 43778 |
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