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Mirrors > Home > ILE Home > Th. List > mulid1d | Unicode version |
Description: Identity law for multiplication. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
addcld.1 |
Ref | Expression |
---|---|
mulid1d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addcld.1 | . 2 | |
2 | mulid1 7116 | . 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: muladd11 7241 ltmul1 7692 mulap0 7744 divrecap 7776 diveqap1 7793 conjmulap 7817 apmul1 7876 qapne 8724 divelunit 9024 modqid 9351 q2submod 9387 addmodlteq 9400 expadd 9518 leexp2r 9530 nnlesq 9578 sqoddm1div8 9625 nn0opthlem1d 9647 faclbnd 9668 faclbnd2 9669 faclbnd6 9671 facavg 9673 bcn0 9682 bcn1 9685 1dvds 10209 bezoutlema 10388 bezoutlemb 10389 gcdmultiple 10409 sqgcd 10418 lcm1 10463 coprmdvds 10474 qredeu 10479 |
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