![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 3decltc | Unicode version |
Description: Comparing two decimal integers with three "digits" (unequal higher places). (Contributed by AV, 15-Jun-2021.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
3decltc.a |
![]() ![]() ![]() ![]() |
3decltc.b |
![]() ![]() ![]() ![]() |
3decltc.c |
![]() ![]() ![]() ![]() |
3decltc.d |
![]() ![]() ![]() ![]() |
3decltc.e |
![]() ![]() ![]() ![]() |
3decltc.f |
![]() ![]() ![]() ![]() |
3decltc.3 |
![]() ![]() ![]() ![]() |
3decltc.1 |
![]() ![]() ![]() ![]() ![]() |
3decltc.2 |
![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
3decltc |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3decltc.a |
. . 3
![]() ![]() ![]() ![]() | |
2 | 3decltc.c |
. . 3
![]() ![]() ![]() ![]() | |
3 | 1, 2 | deccl 9411 |
. 2
![]() ![]() ![]() ![]() ![]() |
4 | 3decltc.b |
. . 3
![]() ![]() ![]() ![]() | |
5 | 3decltc.d |
. . 3
![]() ![]() ![]() ![]() | |
6 | 4, 5 | deccl 9411 |
. 2
![]() ![]() ![]() ![]() ![]() |
7 | 3decltc.e |
. 2
![]() ![]() ![]() ![]() | |
8 | 3decltc.f |
. 2
![]() ![]() ![]() ![]() | |
9 | 3decltc.2 |
. 2
![]() ![]() ![]() ![]() ![]() | |
10 | 3decltc.1 |
. . 3
![]() ![]() ![]() ![]() ![]() | |
11 | 3decltc.3 |
. . 3
![]() ![]() ![]() ![]() | |
12 | 1, 4, 2, 5, 10, 11 | decltc 9425 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() |
13 | 3, 6, 7, 8, 9, 12 | decltc 9425 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-13 2160 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 ax-un 4445 ax-setind 4548 ax-cnex 7915 ax-resscn 7916 ax-1cn 7917 ax-1re 7918 ax-icn 7919 ax-addcl 7920 ax-addrcl 7921 ax-mulcl 7922 ax-mulrcl 7923 ax-addcom 7924 ax-mulcom 7925 ax-addass 7926 ax-mulass 7927 ax-distr 7928 ax-i2m1 7929 ax-0lt1 7930 ax-1rid 7931 ax-0id 7932 ax-rnegex 7933 ax-precex 7934 ax-cnre 7935 ax-pre-ltirr 7936 ax-pre-ltwlin 7937 ax-pre-lttrn 7938 ax-pre-ltadd 7940 ax-pre-mulgt0 7941 |
This theorem depends on definitions: df-bi 117 df-3or 980 df-3an 981 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ne 2358 df-nel 2453 df-ral 2470 df-rex 2471 df-reu 2472 df-rab 2474 df-v 2751 df-sbc 2975 df-dif 3143 df-un 3145 df-in 3147 df-ss 3154 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-int 3857 df-br 4016 df-opab 4077 df-id 4305 df-xp 4644 df-rel 4645 df-cnv 4646 df-co 4647 df-dm 4648 df-iota 5190 df-fun 5230 df-fv 5236 df-riota 5844 df-ov 5891 df-oprab 5892 df-mpo 5893 df-pnf 8007 df-mnf 8008 df-xr 8009 df-ltxr 8010 df-le 8011 df-sub 8143 df-neg 8144 df-inn 8933 df-2 8991 df-3 8992 df-4 8993 df-5 8994 df-6 8995 df-7 8996 df-8 8997 df-9 8998 df-n0 9190 df-z 9267 df-dec 9398 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |