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Mirrors > Home > ILE Home > Th. List > dmres | Unicode version |
Description: The domain of a restriction. Exercise 14 of [TakeutiZaring] p. 25. (Contributed by NM, 1-Aug-1994.) |
Ref | Expression |
---|---|
dmres |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2755 |
. . . . 5
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2 | 1 | eldm2 4843 |
. . . 4
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3 | 19.41v 1914 |
. . . . 5
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4 | vex 2755 |
. . . . . . 7
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5 | 4 | opelres 4930 |
. . . . . 6
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6 | 5 | exbii 1616 |
. . . . 5
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7 | 1 | eldm2 4843 |
. . . . . 6
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8 | 7 | anbi1i 458 |
. . . . 5
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9 | 3, 6, 8 | 3bitr4i 212 |
. . . 4
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10 | 2, 9 | bitr2i 185 |
. . 3
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11 | 10 | ineqri 3343 |
. 2
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12 | incom 3342 |
. 2
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13 | 11, 12 | eqtr3i 2212 |
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 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 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-xp 4650 df-dm 4654 df-res 4656 |
This theorem is referenced by: ssdmres 4947 dmresexg 4948 imadisj 5008 ndmima 5023 imainrect 5092 dmresv 5105 resdmres 5138 funimacnv 5311 fnresdisj 5345 fnres 5351 ssimaex 5598 fnreseql 5647 respreima 5665 ffvresb 5700 fsnunfv 5738 funfvima 5769 offres 6161 smores 6318 smores3 6319 smores2 6320 fnfi 6967 sbthlemi5 6991 sbthlem7 6993 dmaddpi 7355 dmmulpi 7356 fvsetsid 12549 setsfun 12550 setsfun0 12551 setsresg 12553 lmres 14225 metreslem 14357 |
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