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Theorem ecidsn 8702
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 8651 . 2 [𝐴] I = ( I “ {𝐴})
2 imai 6027 . 2 ( I “ {𝐴}) = {𝐴}
31, 2eqtri 2765 1 [𝐴] I = {𝐴}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  {csn 4587   I cid 5531  cima 5637  [cec 8647
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708  ax-sep 5257  ax-nul 5264  ax-pr 5385
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-ral 3066  df-rex 3075  df-rab 3409  df-v 3448  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-br 5107  df-opab 5169  df-id 5532  df-xp 5640  df-rel 5641  df-cnv 5642  df-dm 5644  df-rn 5645  df-res 5646  df-ima 5647  df-ec 8651
This theorem is referenced by:  extid  36774
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