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Mirrors > Home > ILE Home > Th. List > fnres | Unicode version |
Description: An equivalence for functionality of a restriction. Compare dffun8 4872. (Contributed by Mario Carneiro, 20-May-2015.) |
Ref | Expression |
---|---|
fnres |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 253 |
. . 3
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2 | vex 2554 |
. . . . . . . . . 10
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3 | 2 | brres 4561 |
. . . . . . . . 9
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4 | ancom 253 |
. . . . . . . . 9
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5 | 3, 4 | bitri 173 |
. . . . . . . 8
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6 | 5 | mobii 1934 |
. . . . . . 7
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7 | moanimv 1972 |
. . . . . . 7
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8 | 6, 7 | bitri 173 |
. . . . . 6
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9 | 8 | albii 1356 |
. . . . 5
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10 | relres 4582 |
. . . . . 6
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11 | dffun6 4859 |
. . . . . 6
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12 | 10, 11 | mpbiran 846 |
. . . . 5
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13 | df-ral 2305 |
. . . . 5
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14 | 9, 12, 13 | 3bitr4i 201 |
. . . 4
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15 | dmres 4575 |
. . . . . . 7
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16 | inss1 3151 |
. . . . . . 7
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17 | 15, 16 | eqsstri 2969 |
. . . . . 6
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18 | eqss 2954 |
. . . . . 6
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19 | 17, 18 | mpbiran 846 |
. . . . 5
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20 | dfss3 2929 |
. . . . . 6
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21 | 15 | elin2 3121 |
. . . . . . . . 9
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22 | 21 | baib 827 |
. . . . . . . 8
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23 | vex 2554 |
. . . . . . . . 9
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24 | 23 | eldm 4475 |
. . . . . . . 8
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25 | 22, 24 | syl6bb 185 |
. . . . . . 7
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26 | 25 | ralbiia 2332 |
. . . . . 6
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27 | 20, 26 | bitri 173 |
. . . . 5
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28 | 19, 27 | bitri 173 |
. . . 4
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29 | 14, 28 | anbi12i 433 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | r19.26 2435 |
. . 3
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31 | 1, 29, 30 | 3bitr4i 201 |
. 2
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32 | df-fn 4848 |
. 2
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33 | eu5 1944 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
34 | 33 | ralbii 2324 |
. 2
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35 | 31, 32, 34 | 3bitr4i 201 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-sep 3866 ax-pow 3918 ax-pr 3935 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-rex 2306 df-v 2553 df-un 2916 df-in 2918 df-ss 2925 df-pw 3353 df-sn 3373 df-pr 3374 df-op 3376 df-br 3756 df-opab 3810 df-id 4021 df-xp 4294 df-rel 4295 df-cnv 4296 df-co 4297 df-dm 4298 df-res 4300 df-fun 4847 df-fn 4848 |
This theorem is referenced by: f1ompt 5263 |
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