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Theorem ssid 2991
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 𝐴𝐴

Proof of Theorem ssid
Dummy variable 𝑥 is distinct from all other variables.
StepHypRef Expression
1 id 19 . 2 (𝑥𝐴𝑥𝐴)
21ssriv 2976 1 𝐴𝐴
Colors of variables: wff set class
Syntax hints:  wcel 1409  wss 2944
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-in 2951  df-ss 2958
This theorem is referenced by:  eqimssi  3026  eqimss2i  3027  nsspssun  3197  inv1  3280  disjpss  3305  difid  3319  undifabs  3327  pwidg  3399  elssuni  3635  unimax  3641  intmin  3662  rintm  3771  iunpw  4238  sucprcreg  4300  tfisi  4337  peano5  4348  xpss1  4475  xpss2  4476  residm  4669  resdm  4676  resmpt3  4684  ssrnres  4790  dffn3  5080  fimacnv  5323  tfrlem1  5953  rdgss  6000  findcard2d  6378  findcard2sd  6379  1idprl  6745  1idpru  6746  ltexprlemm  6755  elq  8653  expcl  9437  iserclim0  10056
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