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Mirrors > Home > ILE Home > Th. List > 3lt8 | Unicode version |
Description: 3 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013.) |
Ref | Expression |
---|---|
3lt8 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3lt4 8984 |
. 2
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2 | 4lt8 9005 |
. 2
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3 | 3re 8886 |
. . 3
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4 | 4re 8889 |
. . 3
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5 | 8re 8897 |
. . 3
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6 | 3, 4, 5 | lttri 7960 |
. 2
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7 | 1, 2, 6 | mp2an 423 |
1
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Colors of variables: wff set class |
Syntax hints: class class
class wbr 3961 ![]() ![]() ![]() ![]() |
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 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1481 ax-10 1482 ax-11 1483 ax-i12 1484 ax-bndl 1486 ax-4 1487 ax-17 1503 ax-i9 1507 ax-ial 1511 ax-i5r 1512 ax-13 2127 ax-14 2128 ax-ext 2136 ax-sep 4078 ax-pow 4130 ax-pr 4164 ax-un 4388 ax-setind 4490 ax-cnex 7802 ax-resscn 7803 ax-1cn 7804 ax-1re 7805 ax-icn 7806 ax-addcl 7807 ax-addrcl 7808 ax-mulcl 7809 ax-addcom 7811 ax-addass 7813 ax-i2m1 7816 ax-0lt1 7817 ax-0id 7819 ax-rnegex 7820 ax-pre-lttrn 7825 ax-pre-ltadd 7827 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1740 df-eu 2006 df-mo 2007 df-clab 2141 df-cleq 2147 df-clel 2150 df-nfc 2285 df-ne 2325 df-nel 2420 df-ral 2437 df-rex 2438 df-rab 2441 df-v 2711 df-dif 3100 df-un 3102 df-in 3104 df-ss 3111 df-pw 3541 df-sn 3562 df-pr 3563 df-op 3565 df-uni 3769 df-br 3962 df-opab 4022 df-xp 4585 df-iota 5128 df-fv 5171 df-ov 5817 df-pnf 7893 df-mnf 7894 df-ltxr 7896 df-2 8871 df-3 8872 df-4 8873 df-5 8874 df-6 8875 df-7 8876 df-8 8877 |
This theorem is referenced by: 2lt8 9007 |
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