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Mirrors > Home > ILE Home > Th. List > 2timesd | Unicode version |
Description: Two times a number. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
2timesd.1 |
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Ref | Expression |
---|---|
2timesd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2timesd.1 |
. 2
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2 | 2times 8872 |
. 2
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3 | 1, 2 | syl 14 |
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-resscn 7736 ax-1cn 7737 ax-icn 7739 ax-addcl 7740 ax-mulcl 7742 ax-mulcom 7745 ax-mulass 7747 ax-distr 7748 ax-1rid 7751 ax-cnre 7755 |
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-ral 2422 df-rex 2423 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-iota 5096 df-fv 5139 df-ov 5785 df-2 8803 |
This theorem is referenced by: xleaddadd 9700 fzctr 9941 flhalf 10106 q2submod 10189 modaddmodup 10191 m1expeven 10371 binom2 10434 nn0opthlem2d 10499 crre 10661 imval2 10698 resqrexlemdec 10815 amgm2 10922 maxabsle 11008 maxabslemab 11010 maxltsup 11022 max0addsup 11023 arisum2 11300 efival 11475 sinadd 11479 cosadd 11480 addsin 11485 subsin 11486 cosmul 11488 addcos 11489 subcos 11490 sin2t 11492 cos2t 11493 eirraplem 11519 bl2in 12611 cosordlem 12978 apdifflemf 13414 apdifflemr 13415 |
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