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Mirrors > Home > ILE Home > Th. List > mulid2d | Unicode version |
Description: Identity law for multiplication. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
addcld.1 |
Ref | Expression |
---|---|
mulid2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addcld.1 | . 2 | |
2 | mulid2 7764 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 (class class class)co 5774 cc 7618 c1 7621 cmul 7625 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-resscn 7712 ax-1cn 7713 ax-icn 7715 ax-addcl 7716 ax-mulcl 7718 ax-mulcom 7721 ax-mulass 7723 ax-distr 7724 ax-1rid 7727 ax-cnre 7731 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-iota 5088 df-fv 5131 df-ov 5777 |
This theorem is referenced by: adddirp1d 7792 mulsubfacd 8180 mulcanapd 8422 receuap 8430 divdivdivap 8473 divcanap5 8474 subrecap 8598 ltrec 8641 recp1lt1 8657 nndivtr 8762 xp1d2m1eqxm1d2 8972 gtndiv 9146 lincmb01cmp 9786 iccf1o 9787 modqfrac 10110 qnegmod 10142 addmodid 10145 m1expcl2 10315 expgt1 10331 ltexp2a 10345 leexp2a 10346 binom3 10409 faclbnd 10487 facavg 10492 bcval5 10509 cvg1nlemcau 10756 resqrexlemover 10782 resqrexlemcalc2 10787 absimle 10856 maxabslemlub 10979 reccn2ap 11082 binom1p 11254 binom1dif 11256 efcllemp 11364 ef01bndlem 11463 efieq1re 11478 eirraplem 11483 iddvds 11506 gcdaddm 11672 rpmulgcd 11714 prmind2 11801 phiprm 11899 hashgcdlem 11903 dvexp 12844 dvef 12856 sin0pilem1 12862 sinhalfpip 12901 sinhalfpim 12902 coshalfpip 12903 coshalfpim 12904 tangtx 12919 qdencn 13222 |
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