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Mirrors > Home > ILE Home > Th. List > 2pos | Unicode version |
Description: The number 2 is positive. (Contributed by NM, 27-May-1999.) |
Ref | Expression |
---|---|
2pos |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1re 7637 |
. . 3
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2 | 0lt1 7760 |
. . 3
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3 | 1, 1, 2, 2 | addgt0ii 8120 |
. 2
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4 | df-2 8637 |
. 2
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5 | 3, 4 | breqtrri 3900 |
1
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Colors of variables: wff set class |
Syntax hints: class class
class wbr 3875 (class class class)co 5706
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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-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-13 1459 ax-14 1460 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-pow 4038 ax-pr 4069 ax-un 4293 ax-setind 4390 ax-cnex 7586 ax-resscn 7587 ax-1cn 7588 ax-1re 7589 ax-icn 7590 ax-addcl 7591 ax-addrcl 7592 ax-mulcl 7593 ax-addcom 7595 ax-addass 7597 ax-i2m1 7600 ax-0lt1 7601 ax-0id 7603 ax-rnegex 7604 ax-pre-lttrn 7609 ax-pre-ltadd 7611 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-fal 1305 df-nf 1405 df-sb 1704 df-eu 1963 df-mo 1964 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ne 2268 df-nel 2363 df-ral 2380 df-rex 2381 df-rab 2384 df-v 2643 df-dif 3023 df-un 3025 df-in 3027 df-ss 3034 df-pw 3459 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-br 3876 df-opab 3930 df-xp 4483 df-iota 5024 df-fv 5067 df-ov 5709 df-pnf 7674 df-mnf 7675 df-ltxr 7677 df-2 8637 |
This theorem is referenced by: 2ne0 8670 2ap0 8671 3pos 8672 halfgt0 8787 halflt1 8789 halfpos2 8802 halfnneg2 8804 nominpos 8809 avglt1 8810 avglt2 8811 nn0n0n1ge2b 8982 3halfnz 9000 2rp 9296 xleaddadd 9511 2tnp1ge0ge0 9915 mulp1mod1 9979 amgm2 10730 cos2bnd 11265 sin02gt0 11268 sincos2sgn 11270 sin4lt0 11271 epos 11282 oexpneg 11369 oddge22np1 11373 evennn02n 11374 nn0ehalf 11395 nno 11398 nn0oddm1d2 11401 nnoddm1d2 11402 flodddiv4t2lthalf 11429 sqrt2re 11634 sqrt2irrap 11650 bl2in 12331 ex-fl 12540 |
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