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Mirrors > Home > ILE Home > Th. List > 1lt3 | Unicode version |
Description: 1 is less than 3. (Contributed by NM, 26-Sep-2010.) |
Ref | Expression |
---|---|
1lt3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1lt2 8478 |
. 2
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2 | 2lt3 8479 |
. 2
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3 | 1re 7390 |
. . 3
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4 | 2re 8386 |
. . 3
![]() ![]() ![]() ![]() | |
5 | 3re 8390 |
. . 3
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6 | 3, 4, 5 | lttri 7492 |
. 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 3811 ![]() ![]() ![]() ![]() |
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 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-13 1445 ax-14 1446 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 ax-sep 3922 ax-pow 3974 ax-pr 4000 ax-un 4224 ax-setind 4316 ax-cnex 7339 ax-resscn 7340 ax-1cn 7341 ax-1re 7342 ax-icn 7343 ax-addcl 7344 ax-addrcl 7345 ax-mulcl 7346 ax-addcom 7348 ax-addass 7350 ax-i2m1 7353 ax-0lt1 7354 ax-0id 7356 ax-rnegex 7357 ax-pre-lttrn 7362 ax-pre-ltadd 7364 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-fal 1291 df-nf 1391 df-sb 1688 df-eu 1946 df-mo 1947 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ne 2250 df-nel 2345 df-ral 2358 df-rex 2359 df-rab 2362 df-v 2614 df-dif 2986 df-un 2988 df-in 2990 df-ss 2997 df-pw 3408 df-sn 3428 df-pr 3429 df-op 3431 df-uni 3628 df-br 3812 df-opab 3866 df-xp 4407 df-iota 4934 df-fv 4977 df-ov 5594 df-pnf 7427 df-mnf 7428 df-ltxr 7430 df-2 8375 df-3 8376 |
This theorem is referenced by: 1le3 8519 fztpval 9390 expnass 9896 3prm 10890 |
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