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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 7565 |
. . 3
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3 | adddirp1d.b |
. . 3
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4 | 1, 2, 3 | adddird 7574 |
. 2
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5 | 3 | mulid2d 7567 |
. . 3
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6 | 5 | oveq2d 5682 |
. 2
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7 | 4, 6 | eqtrd 2121 |
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-resscn 7498 ax-1cn 7499 ax-icn 7501 ax-addcl 7502 ax-mulcl 7504 ax-mulcom 7507 ax-mulass 7509 ax-distr 7510 ax-1rid 7513 ax-cnre 7517 |
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-ral 2365 df-rex 2366 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-sn 3456 df-pr 3457 df-op 3459 df-uni 3660 df-br 3852 df-iota 4993 df-fv 5036 df-ov 5669 |
This theorem is referenced by: modqvalp1 9811 hashxp 10295 fsumconst 10909 divalglemnqt 11259 |
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