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Mirrors > Home > ILE Home > Th. List > 6lt10 | Unicode version |
Description: 6 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015.) (Revised by AV, 8-Sep-2021.) |
Ref | Expression |
---|---|
6lt10 | ; |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 6lt7 9074 | . 2 | |
2 | 7lt10 9487 | . 2 ; | |
3 | 6re 8971 | . . 3 | |
4 | 7re 8973 | . . 3 | |
5 | 10re 9373 | . . 3 ; | |
6 | 3, 4, 5 | lttri 8036 | . 2 ; ; |
7 | 1, 2, 6 | mp2an 426 | 1 ; |
Colors of variables: wff set class |
Syntax hints: class class class wbr 3998 cc0 7786 c1 7787 clt 7966 c6 8945 c7 8946 ;cdc 9355 |
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 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-10 1503 ax-11 1504 ax-i12 1505 ax-bndl 1507 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 ax-i5r 1533 ax-13 2148 ax-14 2149 ax-ext 2157 ax-sep 4116 ax-pow 4169 ax-pr 4203 ax-un 4427 ax-setind 4530 ax-cnex 7877 ax-resscn 7878 ax-1cn 7879 ax-1re 7880 ax-icn 7881 ax-addcl 7882 ax-addrcl 7883 ax-mulcl 7884 ax-addcom 7886 ax-mulcom 7887 ax-addass 7888 ax-mulass 7889 ax-distr 7890 ax-i2m1 7891 ax-0lt1 7892 ax-1rid 7893 ax-0id 7894 ax-rnegex 7895 ax-cnre 7897 ax-pre-lttrn 7900 ax-pre-ltadd 7902 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1459 df-sb 1761 df-eu 2027 df-mo 2028 df-clab 2162 df-cleq 2168 df-clel 2171 df-nfc 2306 df-ne 2346 df-nel 2441 df-ral 2458 df-rex 2459 df-rab 2462 df-v 2737 df-dif 3129 df-un 3131 df-in 3133 df-ss 3140 df-pw 3574 df-sn 3595 df-pr 3596 df-op 3598 df-uni 3806 df-int 3841 df-br 3999 df-opab 4060 df-xp 4626 df-iota 5170 df-fv 5216 df-ov 5868 df-pnf 7968 df-mnf 7969 df-ltxr 7971 df-inn 8891 df-2 8949 df-3 8950 df-4 8951 df-5 8952 df-6 8953 df-7 8954 df-8 8955 df-9 8956 df-dec 9356 |
This theorem is referenced by: 5lt10 9489 slotsdnscsi 12606 |
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