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Mirrors > Home > ILE Home > Th. List > fnres | Unicode version |
Description: An equivalence for functionality of a restriction. Compare dffun8 5109. (Contributed by Mario Carneiro, 20-May-2015.) |
Ref | Expression |
---|---|
fnres |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 264 |
. . 3
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2 | vex 2660 |
. . . . . . . . . 10
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3 | 2 | brres 4783 |
. . . . . . . . 9
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4 | ancom 264 |
. . . . . . . . 9
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5 | 3, 4 | bitri 183 |
. . . . . . . 8
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6 | 5 | mobii 2012 |
. . . . . . 7
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7 | moanimv 2050 |
. . . . . . 7
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8 | 6, 7 | bitri 183 |
. . . . . 6
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9 | 8 | albii 1429 |
. . . . 5
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10 | relres 4805 |
. . . . . 6
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11 | dffun6 5095 |
. . . . . 6
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12 | 10, 11 | mpbiran 907 |
. . . . 5
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13 | df-ral 2395 |
. . . . 5
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14 | 9, 12, 13 | 3bitr4i 211 |
. . . 4
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15 | dmres 4798 |
. . . . . . 7
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16 | inss1 3262 |
. . . . . . 7
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17 | 15, 16 | eqsstri 3095 |
. . . . . 6
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18 | eqss 3078 |
. . . . . 6
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19 | 17, 18 | mpbiran 907 |
. . . . 5
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20 | dfss3 3053 |
. . . . . 6
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21 | 15 | elin2 3230 |
. . . . . . . . 9
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22 | 21 | baib 887 |
. . . . . . . 8
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23 | vex 2660 |
. . . . . . . . 9
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24 | 23 | eldm 4696 |
. . . . . . . 8
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25 | 22, 24 | syl6bb 195 |
. . . . . . 7
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26 | 25 | ralbiia 2423 |
. . . . . 6
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27 | 20, 26 | bitri 183 |
. . . . 5
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28 | 19, 27 | bitri 183 |
. . . 4
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29 | 14, 28 | anbi12i 453 |
. . 3
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30 | r19.26 2532 |
. . 3
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31 | 1, 29, 30 | 3bitr4i 211 |
. 2
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32 | df-fn 5084 |
. 2
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33 | eu5 2022 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
34 | 33 | ralbii 2415 |
. 2
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35 | 31, 32, 34 | 3bitr4i 211 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-14 1475 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 ax-sep 4006 ax-pow 4058 ax-pr 4091 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-eu 1978 df-mo 1979 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-ral 2395 df-rex 2396 df-v 2659 df-un 3041 df-in 3043 df-ss 3050 df-pw 3478 df-sn 3499 df-pr 3500 df-op 3502 df-br 3896 df-opab 3950 df-id 4175 df-xp 4505 df-rel 4506 df-cnv 4507 df-co 4508 df-dm 4509 df-res 4511 df-fun 5083 df-fn 5084 |
This theorem is referenced by: f1ompt 5525 |
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