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Mirrors > Home > MPE Home > Th. List > mulid1i | Structured version Visualization version Unicode version |
Description: Identity law for multiplication. (Contributed by NM, 14-Feb-1995.) |
Ref | Expression |
---|---|
axi.1 |
Ref | Expression |
---|---|
mulid1i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axi.1 | . 2 | |
2 | mulid1 10037 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 wcel 1990 (class class class)co 6650 cc 9934 c1 9937 cmul 9941 |
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-mulcl 9998 ax-mulcom 10000 ax-mulass 10002 ax-distr 10003 ax-1rid 10006 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-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 |
This theorem is referenced by: addid1 10216 0lt1 10550 muleqadd 10671 1t1e1 11175 2t1e2 11176 3t1e3 11178 halfpm6th 11253 9p1e10 11496 numltc 11528 numsucc 11549 dec10p 11553 dec10pOLD 11554 numadd 11560 numaddc 11561 11multnc 11592 4t3lem 11631 5t2e10 11634 9t11e99 11671 9t11e99OLD 11672 nn0opthlem1 13055 faclbnd4lem1 13080 rei 13896 imi 13897 cji 13899 sqrtm1 14016 0.999... 14612 0.999...OLD 14613 efival 14882 ef01bndlem 14914 3lcm2e6 15440 decsplit0b 15784 decsplit0bOLD 15788 2exp8 15796 37prm 15828 43prm 15829 83prm 15830 139prm 15831 163prm 15832 317prm 15833 1259lem1 15838 1259lem2 15839 1259lem3 15840 1259lem4 15841 1259lem5 15842 2503lem1 15844 2503lem2 15845 2503prm 15847 4001lem1 15848 4001lem2 15849 4001lem3 15850 cnmsgnsubg 19923 mdetralt 20414 dveflem 23742 dvsincos 23744 efhalfpi 24223 pige3 24269 cosne0 24276 efif1olem4 24291 logf1o2 24396 asin1 24621 dvatan 24662 log2ublem3 24675 log2ub 24676 birthday 24681 basellem9 24815 ppiub 24929 chtub 24937 bposlem8 25016 lgsdir2 25055 mulog2sumlem2 25224 pntlemb 25286 avril1 27319 ipidsq 27565 nmopadjlem 28948 nmopcoadji 28960 unierri 28963 sgnmul 30604 signswch 30638 itgexpif 30684 reprlt 30697 breprexp 30711 hgt750lem 30729 hgt750lem2 30730 circum 31568 dvasin 33496 inductionexd 38453 xralrple3 39590 wallispi 40287 wallispi2lem2 40289 stirlinglem1 40291 dirkertrigeqlem3 40317 257prm 41473 fmtno4prmfac193 41485 fmtno5fac 41494 139prmALT 41511 127prm 41515 |
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