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Mirrors > Home > ILE Home > Th. List > 9lt10 | GIF version |
Description: 9 is less than 10. (Contributed by Mario Carneiro, 8-Feb-2015.) (Revised by AV, 8-Sep-2021.) |
Ref | Expression |
---|---|
9lt10 | ⊢ 9 < ;10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 9re 9020 | . . 3 ⊢ 9 ∈ ℝ | |
2 | 1 | ltp1i 8876 | . 2 ⊢ 9 < (9 + 1) |
3 | 9p1e10 9400 | . 2 ⊢ (9 + 1) = ;10 | |
4 | 2, 3 | breqtri 4040 | 1 ⊢ 9 < ;10 |
Colors of variables: wff set class |
Syntax hints: class class class wbr 4015 (class class class)co 5888 0cc0 7825 1c1 7826 + caddc 7828 < clt 8006 9c9 8991 ;cdc 9398 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-13 2160 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 ax-un 4445 ax-setind 4548 ax-cnex 7916 ax-resscn 7917 ax-1cn 7918 ax-1re 7919 ax-icn 7920 ax-addcl 7921 ax-addrcl 7922 ax-mulcl 7923 ax-addcom 7925 ax-mulcom 7926 ax-addass 7927 ax-mulass 7928 ax-distr 7929 ax-i2m1 7930 ax-0lt1 7931 ax-1rid 7932 ax-0id 7933 ax-rnegex 7934 ax-cnre 7936 ax-pre-ltadd 7941 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ne 2358 df-nel 2453 df-ral 2470 df-rex 2471 df-rab 2474 df-v 2751 df-dif 3143 df-un 3145 df-in 3147 df-ss 3154 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-int 3857 df-br 4016 df-opab 4077 df-xp 4644 df-iota 5190 df-fv 5236 df-ov 5891 df-pnf 8008 df-mnf 8009 df-ltxr 8011 df-inn 8934 df-2 8992 df-3 8993 df-4 8994 df-5 8995 df-6 8996 df-7 8997 df-8 8998 df-9 8999 df-dec 9399 |
This theorem is referenced by: 8lt10 9529 slotsdifplendx 12683 dsndxntsetndx 12693 unifndxntsetndx 12700 setsmsdsg 14276 |
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