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Theorem ssid 3290
 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 A

Proof of Theorem ssid
Dummy variable x is distinct from all other variables.
StepHypRef Expression
1 id 19 . 2 (x Ax A)
21ssriv 3277 1 A A
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1710   ⊆ wss 3257 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 This theorem is referenced by:  eqimssi  3325  eqimss2i  3326  nsspssun  3488  inv1  3577  disjpss  3601  difid  3618  pwidg  3734  elssuni  3919  unimax  3925  intmin  3946  rintn0  4056  ssbri  4681  xpss1  4856  xpss2  4857  residm  4994  resdm  4998  dffn3  5229  fimacnv  5411  clos1nrel  5886  ssetpov  5944  lecidg  6196  sbthlem1  6203
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