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Mirrors > Home > ILE Home > Th. List > adddird | Unicode version |
Description: Distributive law (right-distributivity). (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
addcld.1 |
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addcld.2 |
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addassd.3 |
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Ref | Expression |
---|---|
adddird |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addcld.1 |
. 2
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2 | addcld.2 |
. 2
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3 | addassd.3 |
. 2
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4 | adddir 7542 |
. 2
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5 | 1, 2, 3, 4 | syl3anc 1175 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-addcl 7504 ax-mulcom 7509 ax-distr 7512 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-rex 2366 df-v 2624 df-un 3006 df-sn 3458 df-pr 3459 df-op 3461 df-uni 3662 df-br 3854 df-iota 4995 df-fv 5038 df-ov 5671 |
This theorem is referenced by: adddirp1d 7577 joinlmuladdmuld 7578 1p1times 7679 recextlem1 8183 divdirap 8227 subsq 10124 subsq2 10125 binom2 10128 binom3 10134 remullem 10368 resqrexlemover 10506 resqrexlemcalc1 10510 binomlem 10940 |
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