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Theorem ecidsn 6355
Description: An equivalence class modulo the identity relation is a singleton. (Contributed by NM, 24-Oct-2004.)
Assertion
Ref Expression
ecidsn  |-  [ A ]  _I  =  { A }

Proof of Theorem ecidsn
StepHypRef Expression
1 df-ec 6310 . 2  |-  [ A ]  _I  =  (  _I  " { A }
)
2 imai 4803 . 2  |-  (  _I  " { A } )  =  { A }
31, 2eqtri 2109 1  |-  [ A ]  _I  =  { A }
Colors of variables: wff set class
Syntax hints:    = wceq 1290   {csn 3452    _I cid 4126   "cima 4457   [cec 6306
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-14 1451  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071  ax-sep 3965  ax-pow 4017  ax-pr 4047
This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-eu 1952  df-mo 1953  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365  df-rex 2366  df-v 2624  df-un 3006  df-in 3008  df-ss 3015  df-pw 3437  df-sn 3458  df-pr 3459  df-op 3461  df-br 3854  df-opab 3908  df-id 4131  df-xp 4460  df-rel 4461  df-cnv 4462  df-dm 4464  df-rn 4465  df-res 4466  df-ima 4467  df-ec 6310
This theorem is referenced by: (None)
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