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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-res 4521 | . 2 | |
2 | inss1 3266 | . 2 | |
3 | 1, 2 | eqsstri 3099 | 1 |
Colors of variables: wff set class |
Syntax hints: cvv 2660 cin 3040 wss 3041 cxp 4507 cres 4511 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-in 3047 df-ss 3054 df-res 4521 |
This theorem is referenced by: relssres 4827 resexg 4829 iss 4835 cocnvres 5033 relresfld 5038 relcoi1 5040 funres 5134 funres11 5165 funcnvres 5166 2elresin 5204 fssres 5268 foimacnv 5353 tposss 6111 dftpos4 6128 smores 6157 smores2 6159 caserel 6940 txss12 12362 txbasval 12363 |
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