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Mirrors > Home > ILE Home > Th. List > 1p1times | Unicode version |
Description: Two times a number. (Contributed by NM, 18-May-1999.) (Revised by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
1p1times |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1cn 7501 |
. . . 4
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2 | 1 | a1i 9 |
. . 3
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3 | id 19 |
. . 3
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4 | 2, 2, 3 | adddird 7576 |
. 2
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5 | mulid2 7549 |
. . 3
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6 | 5, 5 | oveq12d 5686 |
. 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 7500 ax-1cn 7501 ax-icn 7503 ax-addcl 7504 ax-mulcl 7506 ax-mulcom 7509 ax-mulass 7511 ax-distr 7512 ax-1rid 7515 ax-cnre 7519 |
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 2624 df-un 3006 df-in 3008 df-ss 3015 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: eqneg 8262 2times 8607 |
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