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Mirrors > Home > ILE Home > Th. List > resdm | Unicode version |
Description: A relation restricted to its domain equals itself. (Contributed by NM, 12-Dec-2006.) |
Ref | Expression |
---|---|
resdm |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid 3067 |
. 2
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2 | relssres 4793 |
. 2
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3 | 1, 2 | mpan2 419 |
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 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-14 1460 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-pow 4038 ax-pr 4069 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-v 2643 df-un 3025 df-in 3027 df-ss 3034 df-pw 3459 df-sn 3480 df-pr 3481 df-op 3483 df-br 3876 df-opab 3930 df-xp 4483 df-rel 4484 df-dm 4487 df-res 4489 |
This theorem is referenced by: resindm 4797 resdm2 4965 relresfld 5004 relcoi1 5006 funimaexg 5143 fnex 5574 dftpos2 6088 pmresg 6500 dif1en 6702 |
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