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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 2554 |
. . . . 5
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2 | 1 | eldm2 4476 |
. . . 4
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3 | 19.41v 1779 |
. . . . 5
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4 | vex 2554 |
. . . . . . 7
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5 | 4 | opelres 4560 |
. . . . . 6
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6 | 5 | exbii 1493 |
. . . . 5
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7 | 1 | eldm2 4476 |
. . . . . 6
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8 | 7 | anbi1i 431 |
. . . . 5
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9 | 3, 6, 8 | 3bitr4i 201 |
. . . 4
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10 | 2, 9 | bitr2i 174 |
. . 3
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11 | 10 | ineqri 3124 |
. 2
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12 | incom 3123 |
. 2
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13 | 11, 12 | eqtr3i 2059 |
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-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-xp 4294 df-dm 4298 df-res 4300 |
This theorem is referenced by: ssdmres 4576 dmresexg 4577 imadisj 4630 ndmima 4645 imainrect 4709 dmresv 4722 resdmres 4755 funimacnv 4918 fnresdisj 4952 fnres 4958 ssimaex 5177 fnreseql 5220 respreima 5238 ffvresb 5271 fsnunfv 5306 funfvima 5333 offres 5704 smores 5848 smores3 5849 smores2 5850 dmaddpi 6309 dmmulpi 6310 |
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