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Mirrors > Home > ILE Home > Th. List > 9lt10 | Unicode version |
Description: 9 is less than 10. (Contributed by Mario Carneiro, 8-Feb-2015.) (Revised by AV, 8-Sep-2021.) |
Ref | Expression |
---|---|
9lt10 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 9re 8499 |
. . 3
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2 | 1 | ltp1i 8356 |
. 2
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3 | 9p1e10 8869 |
. 2
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4 | 2, 3 | breqtri 3866 |
1
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Colors of variables: wff set class |
Syntax hints: class class
class wbr 3843 (class class class)co 5644
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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 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-13 1449 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3955 ax-pow 4007 ax-pr 4034 ax-un 4258 ax-setind 4351 ax-cnex 7426 ax-resscn 7427 ax-1cn 7428 ax-1re 7429 ax-icn 7430 ax-addcl 7431 ax-addrcl 7432 ax-mulcl 7433 ax-addcom 7435 ax-mulcom 7436 ax-addass 7437 ax-mulass 7438 ax-distr 7439 ax-i2m1 7440 ax-0lt1 7441 ax-1rid 7442 ax-0id 7443 ax-rnegex 7444 ax-cnre 7446 ax-pre-ltadd 7451 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-fal 1295 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ne 2256 df-nel 2351 df-ral 2364 df-rex 2365 df-rab 2368 df-v 2621 df-dif 3001 df-un 3003 df-in 3005 df-ss 3012 df-pw 3429 df-sn 3450 df-pr 3451 df-op 3453 df-uni 3652 df-int 3687 df-br 3844 df-opab 3898 df-xp 4442 df-iota 4975 df-fv 5018 df-ov 5647 df-pnf 7514 df-mnf 7515 df-ltxr 7517 df-inn 8413 df-2 8471 df-3 8472 df-4 8473 df-5 8474 df-6 8475 df-7 8476 df-8 8477 df-9 8478 df-dec 8868 |
This theorem is referenced by: 8lt10 8998 |
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