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Mirrors > Home > ILE Home > Th. List > mulid2 | Unicode version |
Description: Identity law for multiplication. Note: see mulid1 7116 for commuted version. (Contributed by NM, 8-Oct-1999.) |
Ref | Expression |
---|---|
mulid2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1cn 7069 | . . 3 | |
2 | mulcom 7102 | . . 3 | |
3 | 1, 2 | mpan 414 | . 2 |
4 | mulid1 7116 | . 2 | |
5 | 3, 4 | eqtrd 2113 | 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: mulid2i 7122 mulid2d 7137 muladd11 7241 1p1times 7242 mulm1 7504 div1 7791 recdivap 7806 divdivap2 7812 conjmulap 7817 expp1 9483 recan 9995 gcdadd 10376 gcdid 10377 |
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