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Mirrors > Home > MPE Home > Th. List > setsnid | Structured version Visualization version Unicode version |
Description: Value of the structure replacement function at an untouched index. (Contributed by Mario Carneiro, 1-Dec-2014.) (Revised by Mario Carneiro, 30-Apr-2015.) |
Ref | Expression |
---|---|
setsid.e |
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setsnid.n |
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Ref | Expression |
---|---|
setsnid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | setsid.e |
. . . 4
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2 | id 22 |
. . . 4
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3 | 1, 2 | strfvnd 15184 |
. . 3
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4 | ovex 6342 |
. . . . 5
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5 | 4, 1 | strfvn 15186 |
. . . 4
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6 | setsres 15199 |
. . . . . 6
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7 | 6 | fveq1d 5889 |
. . . . 5
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8 | fvex 5897 |
. . . . . . 7
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9 | setsnid.n |
. . . . . . 7
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10 | eldifsn 4109 |
. . . . . . 7
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11 | 8, 9, 10 | mpbir2an 936 |
. . . . . 6
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12 | fvres 5901 |
. . . . . 6
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13 | 11, 12 | ax-mp 5 |
. . . . 5
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14 | fvres 5901 |
. . . . . 6
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15 | 11, 14 | ax-mp 5 |
. . . . 5
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16 | 7, 13, 15 | 3eqtr3g 2518 |
. . . 4
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17 | 5, 16 | syl5eq 2507 |
. . 3
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18 | 3, 17 | eqtr4d 2498 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 1 | str0 15209 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | fvprc 5881 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | reldmsets 15192 |
. . . . 5
![]() ![]() ![]() | |
22 | 21 | ovprc1 6345 |
. . . 4
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23 | 22 | fveq2d 5891 |
. . 3
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24 | 19, 20, 23 | 3eqtr4a 2521 |
. 2
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25 | 18, 24 | pm2.61i 169 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-8 1899 ax-9 1906 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 ax-sep 4538 ax-nul 4547 ax-pow 4594 ax-pr 4652 ax-un 6609 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-mo 2314 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ne 2634 df-ral 2753 df-rex 2754 df-rab 2757 df-v 3058 df-sbc 3279 df-dif 3418 df-un 3420 df-in 3422 df-ss 3429 df-nul 3743 df-if 3893 df-sn 3980 df-pr 3982 df-op 3986 df-uni 4212 df-br 4416 df-opab 4475 df-mpt 4476 df-id 4767 df-xp 4858 df-rel 4859 df-cnv 4860 df-co 4861 df-dm 4862 df-res 4864 df-iota 5564 df-fun 5602 df-fv 5608 df-ov 6317 df-oprab 6318 df-mpt2 6319 df-slot 15173 df-sets 15175 |
This theorem is referenced by: resslem 15230 oppchomfval 15667 oppcbas 15671 rescbas 15782 rescco 15785 rescabs 15786 odubas 16427 oppglem 17049 mgplem 17776 opprlem 17904 sralem 18448 srasca 18452 sravsca 18453 opsrbaslem 18749 zlmlem 19136 zlmsca 19140 znbaslem 19157 thlbas 19307 thlle 19308 matbas 19486 matplusg 19487 matsca 19488 matvsca 19489 tuslem 21330 setsmsbas 21538 setsmsds 21539 tnglem 21696 tngds 21704 ttgval 24953 ttglem 24954 cchhllem 24965 resvlem 28642 zlmds 28816 zlmtset 28817 hlhilslem 35553 uhgrepe 39962 cznrnglem 40227 cznabel 40228 cznrng 40229 |
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