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Mirrors > Home > ILE Home > Th. List > 3lt7 | Unicode version |
Description: 3 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013.) |
Ref | Expression |
---|---|
3lt7 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3lt4 8499 |
. 2
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2 | 4lt7 8513 |
. 2
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3 | 3re 8408 |
. . 3
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4 | 4re 8411 |
. . 3
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5 | 7re 8417 |
. . 3
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6 | 3, 4, 5 | lttri 7510 |
. 2
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7 | 1, 2, 6 | mp2an 417 |
1
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Colors of variables: wff set class |
Syntax hints: class class
class wbr 3814 ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663 ax-5 1379 ax-7 1380 ax-gen 1381 ax-ie1 1425 ax-ie2 1426 ax-8 1438 ax-10 1439 ax-11 1440 ax-i12 1441 ax-bndl 1442 ax-4 1443 ax-13 1447 ax-14 1448 ax-17 1462 ax-i9 1466 ax-ial 1470 ax-i5r 1471 ax-ext 2067 ax-sep 3925 ax-pow 3977 ax-pr 4003 ax-un 4227 ax-setind 4319 ax-cnex 7357 ax-resscn 7358 ax-1cn 7359 ax-1re 7360 ax-icn 7361 ax-addcl 7362 ax-addrcl 7363 ax-mulcl 7364 ax-addcom 7366 ax-addass 7368 ax-i2m1 7371 ax-0lt1 7372 ax-0id 7374 ax-rnegex 7375 ax-pre-lttrn 7380 ax-pre-ltadd 7382 |
This theorem depends on definitions: df-bi 115 df-3an 924 df-tru 1290 df-fal 1293 df-nf 1393 df-sb 1690 df-eu 1948 df-mo 1949 df-clab 2072 df-cleq 2078 df-clel 2081 df-nfc 2214 df-ne 2252 df-nel 2347 df-ral 2360 df-rex 2361 df-rab 2364 df-v 2616 df-dif 2988 df-un 2990 df-in 2992 df-ss 2999 df-pw 3411 df-sn 3431 df-pr 3432 df-op 3434 df-uni 3631 df-br 3815 df-opab 3869 df-xp 4410 df-iota 4937 df-fv 4980 df-ov 5597 df-pnf 7445 df-mnf 7446 df-ltxr 7448 df-2 8393 df-3 8394 df-4 8395 df-5 8396 df-6 8397 df-7 8398 |
This theorem is referenced by: 2lt7 8515 |
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