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Mirrors > Home > ILE Home > Th. List > muladdd | Unicode version |
Description: Product of two sums. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
mulm1d.1 | |
mulnegd.2 | |
subdid.3 | |
muladdd.4 |
Ref | Expression |
---|---|
muladdd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mulm1d.1 | . 2 | |
2 | mulnegd.2 | . 2 | |
3 | subdid.3 | . 2 | |
4 | muladdd.4 | . 2 | |
5 | muladd 7488 | . 2 | |
6 | 1, 2, 3, 4, 5 | syl22anc 1170 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 wcel 1433 (class class class)co 5532 cc 6979 caddc 6984 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-addcl 7072 ax-mulcl 7074 ax-addcom 7076 ax-mulcom 7077 ax-addass 7078 ax-distr 7080 |
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-rex 2354 df-v 2603 df-un 2977 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: mulreim 7704 |
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