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Mirrors > Home > ILE Home > Th. List > fzdifsuc | Unicode version |
Description: Remove a successor from the end of a finite set of sequential integers. (Contributed by AV, 4-Sep-2019.) |
Ref | Expression |
---|---|
fzdifsuc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfzelz 9837 |
. . 3
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2 | 1 | adantl 275 |
. 2
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3 | eldifi 3203 |
. . . 4
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4 | elfzelz 9837 |
. . . 4
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5 | 3, 4 | syl 14 |
. . 3
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6 | 5 | adantl 275 |
. 2
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7 | simpr 109 |
. . . 4
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8 | eluzel2 9355 |
. . . . 5
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9 | 8 | adantr 274 |
. . . 4
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10 | eluzelz 9359 |
. . . . 5
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11 | 10 | adantr 274 |
. . . 4
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12 | elfz 9827 |
. . . 4
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13 | 7, 9, 11, 12 | syl3anc 1217 |
. . 3
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14 | eldif 3085 |
. . . . . . 7
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15 | 11 | peano2zd 9200 |
. . . . . . . . 9
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16 | elfz 9827 |
. . . . . . . . 9
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17 | 7, 9, 15, 16 | syl3anc 1217 |
. . . . . . . 8
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18 | velsn 3549 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | 18 | notbii 658 |
. . . . . . . . . 10
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20 | nesym 2354 |
. . . . . . . . . 10
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21 | 19, 20 | bitr4i 186 |
. . . . . . . . 9
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22 | 21 | a1i 9 |
. . . . . . . 8
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23 | 17, 22 | anbi12d 465 |
. . . . . . 7
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24 | 14, 23 | syl5bb 191 |
. . . . . 6
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25 | anass 399 |
. . . . . 6
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26 | 24, 25 | syl6bb 195 |
. . . . 5
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27 | zltlen 9153 |
. . . . . . 7
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28 | 7, 15, 27 | syl2anc 409 |
. . . . . 6
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29 | 28 | anbi2d 460 |
. . . . 5
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30 | 26, 29 | bitr4d 190 |
. . . 4
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31 | zleltp1 9133 |
. . . . . 6
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32 | 7, 11, 31 | syl2anc 409 |
. . . . 5
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33 | 32 | anbi2d 460 |
. . . 4
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34 | 30, 33 | bitr4d 190 |
. . 3
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35 | 13, 34 | bitr4d 190 |
. 2
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36 | 2, 6, 35 | eqrdav 2139 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-un 4363 ax-setind 4460 ax-cnex 7735 ax-resscn 7736 ax-1cn 7737 ax-1re 7738 ax-icn 7739 ax-addcl 7740 ax-addrcl 7741 ax-mulcl 7742 ax-mulrcl 7743 ax-addcom 7744 ax-mulcom 7745 ax-addass 7746 ax-mulass 7747 ax-distr 7748 ax-i2m1 7749 ax-0lt1 7750 ax-1rid 7751 ax-0id 7752 ax-rnegex 7753 ax-precex 7754 ax-cnre 7755 ax-pre-ltirr 7756 ax-pre-ltwlin 7757 ax-pre-lttrn 7758 ax-pre-apti 7759 ax-pre-ltadd 7760 ax-pre-mulgt0 7761 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-nel 2405 df-ral 2422 df-rex 2423 df-reu 2424 df-rab 2426 df-v 2691 df-sbc 2914 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-int 3780 df-br 3938 df-opab 3998 df-mpt 3999 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 df-iota 5096 df-fun 5133 df-fn 5134 df-f 5135 df-fv 5139 df-riota 5738 df-ov 5785 df-oprab 5786 df-mpo 5787 df-pnf 7826 df-mnf 7827 df-xr 7828 df-ltxr 7829 df-le 7830 df-sub 7959 df-neg 7960 df-reap 8361 df-ap 8368 df-inn 8745 df-n0 9002 df-z 9079 df-uz 9351 df-fz 9822 |
This theorem is referenced by: (None) |
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