![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 2pos | Unicode version |
Description: The number 2 is positive. (Contributed by NM, 27-May-1999.) |
Ref | Expression |
---|---|
2pos |
![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1re 7958 |
. . 3
![]() ![]() ![]() ![]() | |
2 | 0lt1 8086 |
. . 3
![]() ![]() ![]() ![]() | |
3 | 1, 1, 2, 2 | addgt0ii 8450 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | df-2 8980 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 3, 4 | breqtrri 4032 |
1
![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: class class
class wbr 4005 (class class class)co 5877
![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4123 ax-pow 4176 ax-pr 4211 ax-un 4435 ax-setind 4538 ax-cnex 7904 ax-resscn 7905 ax-1cn 7906 ax-1re 7907 ax-icn 7908 ax-addcl 7909 ax-addrcl 7910 ax-mulcl 7911 ax-addcom 7913 ax-addass 7915 ax-i2m1 7918 ax-0lt1 7919 ax-0id 7921 ax-rnegex 7922 ax-pre-lttrn 7927 ax-pre-ltadd 7929 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2741 df-dif 3133 df-un 3135 df-in 3137 df-ss 3144 df-pw 3579 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-br 4006 df-opab 4067 df-xp 4634 df-iota 5180 df-fv 5226 df-ov 5880 df-pnf 7996 df-mnf 7997 df-ltxr 7999 df-2 8980 |
This theorem is referenced by: 2ne0 9013 2ap0 9014 3pos 9015 halfgt0 9136 halflt1 9138 halfpos2 9151 halfnneg2 9153 nominpos 9158 avglt1 9159 avglt2 9160 nn0n0n1ge2b 9334 3halfnz 9352 2rp 9660 xleaddadd 9889 2tnp1ge0ge0 10303 mulp1mod1 10367 amgm2 11129 cos2bnd 11770 sin02gt0 11773 sincos2sgn 11775 sin4lt0 11776 epos 11790 oexpneg 11884 oddge22np1 11888 evennn02n 11889 nn0ehalf 11910 nno 11913 nn0oddm1d2 11916 nnoddm1d2 11917 flodddiv4t2lthalf 11944 sqrt2re 12165 sqrt2irrap 12182 slotsdifdsndx 12681 bl2in 13988 pilem3 14289 pipos 14294 sinhalfpilem 14297 sincosq1lem 14331 sinq12gt0 14336 coseq00topi 14341 coseq0negpitopi 14342 tangtx 14344 sincos4thpi 14346 tan4thpi 14347 sincos6thpi 14348 cosordlem 14355 cos02pilt1 14357 lgseisenlem1 14535 lgseisenlem2 14536 ex-fl 14562 |
Copyright terms: Public domain | W3C validator |