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Theorem ssid 3042
Description: Any class is a subclass of itself. Exercise 10 of [TakeutiZaring] p. 18. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
ssid  |-  A  C_  A

Proof of Theorem ssid
Dummy variable  x is distinct from all other variables.
StepHypRef Expression
1 id 19 . 2  |-  ( x  e.  A  ->  x  e.  A )
21ssriv 3027 1  |-  A  C_  A
Colors of variables: wff set class
Syntax hints:    e. wcel 1438    C_ wss 2997
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3003  df-ss 3010
This theorem is referenced by:  ssidd  3043  eqimssi  3078  eqimss2i  3079  inv1  3316  difid  3348  undifabs  3356  pwidg  3438  elssuni  3676  unimax  3682  intmin  3703  rintm  3813  iunpw  4292  sucprcreg  4355  tfisi  4392  peano5  4403  xpss1  4536  xpss2  4537  residm  4731  resdm  4738  resmpt3  4748  ssrnres  4860  cocnvss  4943  dffn3  5156  fimacnv  5412  foima2  5512  tfrlem1  6055  rdgss  6130  fpmg  6411  findcard2d  6587  findcard2sd  6588  f1finf1o  6635  fidcenumlemr  6643  casef  6758  nnnninf  6785  1idprl  7128  1idpru  7129  ltexprlemm  7138  elq  9076  expcl  9938  serclim0  10657  iserclim0  10658  fsum2d  10792  fsumabs  10822  fsumiun  10833
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