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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 2560 |
. . . . 5
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2 | 1 | eldm2 4533 |
. . . 4
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3 | 19.41v 1782 |
. . . . 5
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4 | vex 2560 |
. . . . . . 7
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5 | 4 | opelres 4617 |
. . . . . 6
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6 | 5 | exbii 1496 |
. . . . 5
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7 | 1 | eldm2 4533 |
. . . . . 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 3130 |
. 2
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12 | incom 3129 |
. 2
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13 | 11, 12 | eqtr3i 2062 |
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 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-xp 4351 df-dm 4355 df-res 4357 |
This theorem is referenced by: ssdmres 4633 dmresexg 4634 imadisj 4687 ndmima 4702 imainrect 4766 dmresv 4779 resdmres 4812 funimacnv 4975 fnresdisj 5009 fnres 5015 ssimaex 5234 fnreseql 5277 respreima 5295 ffvresb 5328 fsnunfv 5363 funfvima 5390 offres 5762 smores 5907 smores3 5908 smores2 5909 dmaddpi 6423 dmmulpi 6424 |
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