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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 7117 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 wcel 1433 (class class class)co 5532 cc 6979 c1 6982 cmul 6986 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-resscn 7068 ax-1cn 7069 ax-icn 7071 ax-addcl 7072 ax-mulcl 7074 ax-mulcom 7077 ax-mulass 7079 ax-distr 7080 ax-1rid 7083 ax-cnre 7087 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-iota 4887 df-fv 4930 df-ov 5535 |
This theorem is referenced by: adddirp1d 7145 mulsubfacd 7522 mulcanapd 7751 receuap 7759 divdivdivap 7801 divcanap5 7802 ltrec 7961 recp1lt1 7977 nndivtr 8080 xp1d2m1eqxm1d2 8283 gtndiv 8442 lincmb01cmp 9025 iccf1o 9026 modqfrac 9339 qnegmod 9371 addmodid 9374 m1expcl2 9498 expgt1 9514 ltexp2a 9528 leexp2a 9529 binom3 9590 faclbnd 9668 facavg 9673 ibcval5 9690 cvg1nlemcau 9870 resqrexlemover 9896 resqrexlemcalc2 9901 absimle 9970 maxabslemlub 10093 iddvds 10208 gcdaddm 10375 rpmulgcd 10415 prmind2 10502 qdencn 10785 |
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