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Mirrors > Home > ILE Home > Th. List > 6lt7 | GIF version |
Description: 6 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013.) |
Ref | Expression |
---|---|
6lt7 | ⊢ 6 < 7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 6re 8187 | . . 3 ⊢ 6 ∈ ℝ | |
2 | 1 | ltp1i 8050 | . 2 ⊢ 6 < (6 + 1) |
3 | df-7 8170 | . 2 ⊢ 7 = (6 + 1) | |
4 | 2, 3 | breqtrri 3818 | 1 ⊢ 6 < 7 |
Colors of variables: wff set class |
Syntax hints: class class class wbr 3793 (class class class)co 5543 1c1 7044 + caddc 7046 < clt 7215 6c6 8160 7c7 8161 |
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 2064 ax-sep 3904 ax-pow 3956 ax-pr 3972 ax-un 4196 ax-setind 4288 ax-cnex 7129 ax-resscn 7130 ax-1cn 7131 ax-1re 7132 ax-icn 7133 ax-addcl 7134 ax-addrcl 7135 ax-mulcl 7136 ax-addcom 7138 ax-addass 7140 ax-i2m1 7143 ax-0lt1 7144 ax-0id 7146 ax-rnegex 7147 ax-pre-ltadd 7154 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-fal 1291 df-nf 1391 df-sb 1687 df-eu 1945 df-mo 1946 df-clab 2069 df-cleq 2075 df-clel 2078 df-nfc 2209 df-ne 2247 df-nel 2341 df-ral 2354 df-rex 2355 df-rab 2358 df-v 2604 df-dif 2976 df-un 2978 df-in 2980 df-ss 2987 df-pw 3392 df-sn 3412 df-pr 3413 df-op 3415 df-uni 3610 df-br 3794 df-opab 3848 df-xp 4377 df-iota 4897 df-fv 4940 df-ov 5546 df-pnf 7217 df-mnf 7218 df-ltxr 7220 df-2 8165 df-3 8166 df-4 8167 df-5 8168 df-6 8169 df-7 8170 |
This theorem is referenced by: 5lt7 8284 6lt8 8290 6lt9 8298 6lt10 8691 |
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