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Mirrors > Home > ILE Home > Th. List > fnres | Unicode version |
Description: An equivalence for functionality of a restriction. Compare dffun8 5259. (Contributed by Mario Carneiro, 20-May-2015.) |
Ref | Expression |
---|---|
fnres |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 266 |
. . 3
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2 | vex 2755 |
. . . . . . . . . 10
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3 | 2 | brres 4928 |
. . . . . . . . 9
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4 | ancom 266 |
. . . . . . . . 9
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5 | 3, 4 | bitri 184 |
. . . . . . . 8
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6 | 5 | mobii 2075 |
. . . . . . 7
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7 | moanimv 2113 |
. . . . . . 7
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8 | 6, 7 | bitri 184 |
. . . . . 6
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9 | 8 | albii 1481 |
. . . . 5
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10 | relres 4950 |
. . . . . 6
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11 | dffun6 5245 |
. . . . . 6
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12 | 10, 11 | mpbiran 942 |
. . . . 5
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13 | df-ral 2473 |
. . . . 5
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14 | 9, 12, 13 | 3bitr4i 212 |
. . . 4
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15 | dmres 4943 |
. . . . . . 7
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16 | inss1 3370 |
. . . . . . 7
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17 | 15, 16 | eqsstri 3202 |
. . . . . 6
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18 | eqss 3185 |
. . . . . 6
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19 | 17, 18 | mpbiran 942 |
. . . . 5
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20 | dfss3 3160 |
. . . . . 6
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21 | 15 | elin2 3338 |
. . . . . . . . 9
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22 | 21 | baib 920 |
. . . . . . . 8
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23 | vex 2755 |
. . . . . . . . 9
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24 | 23 | eldm 4839 |
. . . . . . . 8
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25 | 22, 24 | bitrdi 196 |
. . . . . . 7
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26 | 25 | ralbiia 2504 |
. . . . . 6
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27 | 20, 26 | bitri 184 |
. . . . 5
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28 | 19, 27 | bitri 184 |
. . . 4
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29 | 14, 28 | anbi12i 460 |
. . 3
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30 | r19.26 2616 |
. . 3
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31 | 1, 29, 30 | 3bitr4i 212 |
. 2
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32 | df-fn 5234 |
. 2
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33 | eu5 2085 |
. . 3
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34 | 33 | ralbii 2496 |
. 2
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35 | 31, 32, 34 | 3bitr4i 212 |
1
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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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4189 ax-pr 4224 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-opab 4080 df-id 4308 df-xp 4647 df-rel 4648 df-cnv 4649 df-co 4650 df-dm 4651 df-res 4653 df-fun 5233 df-fn 5234 |
This theorem is referenced by: f1ompt 5683 |
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