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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 4635 |
. 2
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2 | inss1 3355 |
. 2
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3 | 1, 2 | eqsstri 3187 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-in 3135 df-ss 3142 df-res 4635 |
This theorem is referenced by: relssres 4941 resexg 4943 iss 4949 cocnvres 5149 relresfld 5154 relcoi1 5156 funres 5253 funres11 5284 funcnvres 5285 2elresin 5323 fssres 5387 foimacnv 5475 tposss 6241 dftpos4 6258 smores 6287 smores2 6289 caserel 7080 txss12 13430 txbasval 13431 |
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