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Mirrors > Home > ILE Home > Th. List > 3lt4 | Unicode version |
Description: 3 is less than 4. (Contributed by Mario Carneiro, 15-Sep-2013.) |
Ref | Expression |
---|---|
3lt4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3re 8787 | . . 3 | |
2 | 1 | ltp1i 8656 | . 2 |
3 | df-4 8774 | . 2 | |
4 | 2, 3 | breqtrri 3950 | 1 |
Colors of variables: wff set class |
Syntax hints: class class class wbr 3924 (class class class)co 5767 c1 7614 caddc 7616 clt 7793 c3 8765 c4 8766 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 ax-setind 4447 ax-cnex 7704 ax-resscn 7705 ax-1cn 7706 ax-1re 7707 ax-icn 7708 ax-addcl 7709 ax-addrcl 7710 ax-mulcl 7711 ax-addcom 7713 ax-addass 7715 ax-i2m1 7718 ax-0lt1 7719 ax-0id 7721 ax-rnegex 7722 ax-pre-ltadd 7729 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ne 2307 df-nel 2402 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-xp 4540 df-iota 5083 df-fv 5126 df-ov 5770 df-pnf 7795 df-mnf 7796 df-ltxr 7798 df-2 8772 df-3 8773 df-4 8774 |
This theorem is referenced by: 2lt4 8886 3lt5 8889 3lt6 8894 3lt7 8900 3lt8 8907 3lt9 8915 3halfnz 9141 3lt10 9311 fldiv4p1lem1div2 10071 ef01bndlem 11452 sin01bnd 11453 flodddiv4 11620 srngstrd 12070 dveflem 12844 tangtx 12908 ex-fl 12926 |
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