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Mirrors > Home > ILE Home > Th. List > adddirp1d | Unicode version |
Description: Distributive law, plus 1 version. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
adddirp1d.a |
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adddirp1d.b |
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Ref | Expression |
---|---|
adddirp1d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | adddirp1d.a |
. . 3
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2 | 1cnd 8004 |
. . 3
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3 | adddirp1d.b |
. . 3
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4 | 1, 2, 3 | adddird 8014 |
. 2
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5 | 3 | mulid2d 8007 |
. . 3
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6 | 5 | oveq2d 5913 |
. 2
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7 | 4, 6 | eqtrd 2222 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-resscn 7934 ax-1cn 7935 ax-icn 7937 ax-addcl 7938 ax-mulcl 7940 ax-mulcom 7943 ax-mulass 7945 ax-distr 7946 ax-1rid 7949 ax-cnre 7953 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-iota 5196 df-fv 5243 df-ov 5900 |
This theorem is referenced by: modqvalp1 10376 hashxp 10841 fsumconst 11497 divalglemnqt 11960 pcexp 12344 mulgnnass 13114 cnfldmulg 13896 2lgsoddprmlem3d 14936 |
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