Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
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 11091 | . 2 ⊢ 2 ∈ ℂ | |
2 | 1 | mulid1i 10042 | 1 ⊢ (2 · 1) = 2 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 (class class class)co 6650 1c1 9937 · cmul 9941 2c2 11070 |
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-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 |
This theorem is referenced by: decbin2 11683 expubnd 12921 sqrlem7 13989 trirecip 14595 bpoly3 14789 fsumcube 14791 ege2le3 14820 cos2tsin 14909 cos2bnd 14918 odd2np1 15065 opoe 15087 flodddiv4 15137 pythagtriplem4 15524 2503lem2 15845 2503lem3 15846 4001lem4 15851 4001prm 15852 htpycc 22779 pco1 22815 pcohtpylem 22819 pcopt 22822 pcorevlem 22826 ovolunlem1a 23264 cos2pi 24228 coskpi 24272 dcubic1lem 24570 dcubic2 24571 dcubic 24573 mcubic 24574 basellem3 24809 chtublem 24936 bcp1ctr 25004 bclbnd 25005 bposlem1 25009 bposlem2 25010 bposlem5 25013 2lgslem3d1 25128 chebbnd1lem1 25158 chebbnd1lem3 25160 chebbnd1 25161 frgrregord013 27253 ex-ind-dvds 27318 knoppndvlem12 32514 heiborlem6 33615 jm2.23 37563 sumnnodd 39862 wallispilem4 40285 wallispi2lem1 40288 wallispi2lem2 40289 wallispi2 40290 stirlinglem11 40301 dirkertrigeqlem1 40315 fouriersw 40448 fmtnorec4 41461 lighneallem2 41523 lighneallem3 41524 3exp4mod41 41533 opoeALTV 41594 |
Copyright terms: Public domain | W3C validator |