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Theorem ecidsn 6219
 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 6174 . 2 [𝐴] I = ( I “ {𝐴})
2 imai 4711 . 2 ( I “ {𝐴}) = {𝐴}
31, 2eqtri 2102 1 [𝐴] I = {𝐴}
 Colors of variables: wff set class Syntax hints:   = wceq 1285  {csn 3406   I cid 4051   “ cima 4374  [cec 6170 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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-id 4056  df-xp 4377  df-rel 4378  df-cnv 4379  df-dm 4381  df-rn 4382  df-res 4383  df-ima 4384  df-ec 6174 This theorem is referenced by: (None)
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