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Theorem resss 4988
 Description: A class includes its restriction. Exercise 15 of [TakeutiZaring] p. 25. (Contributed by set.mm contributors, 2-Aug-1994.)
Assertion
Ref Expression
resss

Proof of Theorem resss
StepHypRef Expression
1 df-res 4788 . 2
2 inss1 3475 . 2
31, 2eqsstri 3301 1
 Colors of variables: wff setvar class Syntax hints:  cvv 2859   cin 3208   wss 3257   cxp 4770   cres 4774 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-res 4788 This theorem is referenced by:  ssreseq  4997  iss  5000  funres  5143  funres11  5164  funcnvres  5165  2elresin  5194  fssres  5238  foimacnv  5303
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