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Mirrors > Home > ILE Home > Th. List > zextle | Unicode version |
Description: An extensionality-like property for integer ordering. (Contributed by NM, 29-Oct-2005.) |
Ref | Expression |
---|---|
zextle |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zre 8754 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 1 | leidd 7992 |
. . . . . . . 8
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3 | 2 | adantr 270 |
. . . . . . 7
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4 | breq1 3848 |
. . . . . . . . 9
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5 | breq1 3848 |
. . . . . . . . 9
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6 | 4, 5 | bibi12d 233 |
. . . . . . . 8
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7 | 6 | rspcva 2720 |
. . . . . . 7
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8 | 3, 7 | mpbid 145 |
. . . . . 6
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9 | 8 | adantlr 461 |
. . . . 5
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10 | zre 8754 |
. . . . . . . . 9
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11 | 10 | leidd 7992 |
. . . . . . . 8
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12 | 11 | adantr 270 |
. . . . . . 7
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13 | breq1 3848 |
. . . . . . . . 9
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14 | breq1 3848 |
. . . . . . . . 9
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15 | 13, 14 | bibi12d 233 |
. . . . . . . 8
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16 | 15 | rspcva 2720 |
. . . . . . 7
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17 | 12, 16 | mpbird 165 |
. . . . . 6
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18 | 17 | adantll 460 |
. . . . 5
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19 | 9, 18 | jca 300 |
. . . 4
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20 | 19 | ex 113 |
. . 3
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21 | letri3 7566 |
. . . 4
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22 | 1, 10, 21 | syl2an 283 |
. . 3
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23 | 20, 22 | sylibrd 167 |
. 2
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24 | 23 | 3impia 1140 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 3957 ax-pow 4009 ax-pr 4036 ax-un 4260 ax-setind 4353 ax-cnex 7436 ax-resscn 7437 ax-pre-ltirr 7457 ax-pre-apti 7460 |
This theorem depends on definitions: df-bi 115 df-3or 925 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 3431 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-br 3846 df-opab 3900 df-xp 4444 df-cnv 4446 df-iota 4980 df-fv 5023 df-ov 5655 df-pnf 7524 df-mnf 7525 df-xr 7526 df-ltxr 7527 df-le 7528 df-neg 7656 df-z 8751 |
This theorem is referenced by: zextlt 8838 |
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