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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 7781 |
. 2
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5 | 1, 2, 3, 4 | syl3anc 1217 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-addcl 7740 ax-mulcom 7745 ax-distr 7748 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-iota 5096 df-fv 5139 df-ov 5785 |
This theorem is referenced by: adddirp1d 7816 joinlmuladdmuld 7817 1p1times 7920 recextlem1 8436 divdirap 8481 subsq 10430 subsq2 10431 binom2 10434 binom3 10440 remullem 10675 resqrexlemover 10814 resqrexlemcalc1 10818 bdtrilem 11042 binomlem 11284 dvexp 12883 rpcxpadd 13034 |
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