![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 7pos | Unicode version |
Description: The number 7 is positive. (Contributed by NM, 27-May-1999.) |
Ref | Expression |
---|---|
7pos |
![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 6re 8976 |
. . 3
![]() ![]() ![]() ![]() | |
2 | 1re 7934 |
. . 3
![]() ![]() ![]() ![]() | |
3 | 6pos 8996 |
. . 3
![]() ![]() ![]() ![]() | |
4 | 0lt1 8061 |
. . 3
![]() ![]() ![]() ![]() | |
5 | 1, 2, 3, 4 | addgt0ii 8425 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | df-7 8959 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 5, 6 | breqtrri 4027 |
1
![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: class class
class wbr 4000 (class class class)co 5868
![]() ![]() ![]() ![]() ![]() ![]() |
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 4118 ax-pow 4171 ax-pr 4205 ax-un 4429 ax-setind 4532 ax-cnex 7880 ax-resscn 7881 ax-1cn 7882 ax-1re 7883 ax-icn 7884 ax-addcl 7885 ax-addrcl 7886 ax-mulcl 7887 ax-addcom 7889 ax-addass 7891 ax-i2m1 7894 ax-0lt1 7895 ax-0id 7897 ax-rnegex 7898 ax-pre-lttrn 7903 ax-pre-ltadd 7905 |
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 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-xp 4628 df-iota 5173 df-fv 5219 df-ov 5871 df-pnf 7971 df-mnf 7972 df-ltxr 7974 df-2 8954 df-3 8955 df-4 8956 df-5 8957 df-6 8958 df-7 8959 |
This theorem is referenced by: 8pos 8998 lgsdir2lem1 14062 |
Copyright terms: Public domain | W3C validator |