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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 7757 | . 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 5767 cc 7611 c1 7614 cmul 7618 |
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 2119 ax-resscn 7705 ax-1cn 7706 ax-icn 7708 ax-addcl 7709 ax-mulcl 7711 ax-mulcom 7714 ax-mulass 7716 ax-distr 7717 ax-1rid 7720 ax-cnre 7724 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-iota 5083 df-fv 5126 df-ov 5770 |
This theorem is referenced by: adddirp1d 7785 mulsubfacd 8173 mulcanapd 8415 receuap 8423 divdivdivap 8466 divcanap5 8467 subrecap 8591 ltrec 8634 recp1lt1 8650 nndivtr 8755 xp1d2m1eqxm1d2 8965 gtndiv 9139 lincmb01cmp 9779 iccf1o 9780 modqfrac 10103 qnegmod 10135 addmodid 10138 m1expcl2 10308 expgt1 10324 ltexp2a 10338 leexp2a 10339 binom3 10402 faclbnd 10480 facavg 10485 bcval5 10502 cvg1nlemcau 10749 resqrexlemover 10775 resqrexlemcalc2 10780 absimle 10849 maxabslemlub 10972 reccn2ap 11075 binom1p 11247 binom1dif 11249 efcllemp 11353 ef01bndlem 11452 efieq1re 11467 eirraplem 11472 iddvds 11495 gcdaddm 11661 rpmulgcd 11703 prmind2 11790 phiprm 11888 hashgcdlem 11892 dvexp 12833 dvef 12845 sin0pilem1 12851 sinhalfpip 12890 sinhalfpim 12891 coshalfpip 12892 coshalfpim 12893 tangtx 12908 qdencn 13211 |
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