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Mirrors > Home > ILE Home > Th. List > resss | Unicode version |
Description: A class includes its restriction. Exercise 15 of [TakeutiZaring] p. 25. (Contributed by NM, 2-Aug-1994.) |
Ref | Expression |
---|---|
resss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-res 4559 |
. 2
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2 | inss1 3301 |
. 2
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3 | 1, 2 | eqsstri 3134 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-in 3082 df-ss 3089 df-res 4559 |
This theorem is referenced by: relssres 4865 resexg 4867 iss 4873 cocnvres 5071 relresfld 5076 relcoi1 5078 funres 5172 funres11 5203 funcnvres 5204 2elresin 5242 fssres 5306 foimacnv 5393 tposss 6151 dftpos4 6168 smores 6197 smores2 6199 caserel 6980 txss12 12474 txbasval 12475 |
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