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Mirrors > Home > ILE Home > Th. List > times2 | Unicode version |
Description: A number times 2. (Contributed by NM, 16-Oct-2007.) |
Ref | Expression |
---|---|
times2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2cn 8387 |
. . 3
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2 | mulcom 7374 |
. . 3
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3 | 1, 2 | mpan2 416 |
. 2
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4 | 2times 8437 |
. 2
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5 | 3, 4 | eqtrd 2115 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 ax-resscn 7340 ax-1cn 7341 ax-1re 7342 ax-icn 7343 ax-addcl 7344 ax-addrcl 7345 ax-mulcl 7346 ax-mulcom 7349 ax-mulass 7351 ax-distr 7352 ax-1rid 7355 ax-cnre 7359 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ral 2358 df-rex 2359 df-v 2614 df-un 2988 df-in 2990 df-ss 2997 df-sn 3428 df-pr 3429 df-op 3431 df-uni 3628 df-br 3812 df-iota 4934 df-fv 4977 df-ov 5594 df-2 8375 |
This theorem is referenced by: times2i 8440 avglt1 8546 times2d 8551 |
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