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Theorem resss 4635
 Description: A class includes its restriction. Exercise 15 of [TakeutiZaring] p. 25. (Contributed by NM, 2-Aug-1994.)
Assertion
Ref Expression
resss

Proof of Theorem resss
StepHypRef Expression
1 df-res 4357 . 2
2 inss1 3157 . 2
31, 2eqsstri 2975 1
 Colors of variables: wff set class Syntax hints:  cvv 2557   cin 2916   wss 2917   cxp 4343   cres 4347 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-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924  df-ss 2931  df-res 4357 This theorem is referenced by:  relssres  4648  resexg  4650  iss  4654  relresfld  4847  relcoi1  4849  funres  4941  funres11  4971  funcnvres  4972  2elresin  5010  fssres  5066  foimacnv  5144  tposss  5861  dftpos4  5878  smores  5907  smores2  5909
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