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Theorem ecid 6235
 Description: A set is equal to its converse epsilon coset. (Note: converse epsilon is not an equivalence relation.) (Contributed by NM, 13-Aug-1995.) (Revised by Mario Carneiro, 9-Jul-2014.)
Hypothesis
Ref Expression
ecid.1
Assertion
Ref Expression
ecid

Proof of Theorem ecid
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2605 . . . 4
2 ecid.1 . . . 4
31, 2elec 6211 . . 3
42, 1brcnv 4546 . . 3
52epelc 4054 . . 3
63, 4, 53bitri 204 . 2
76eqriv 2079 1
 Colors of variables: wff set class Syntax hints:   wceq 1285   wcel 1434  cvv 2602   class class class wbr 3793   cep 4050  ccnv 4370  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-sbc 2817  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-eprel 4052  df-xp 4377  df-cnv 4379  df-dm 4381  df-rn 4382  df-res 4383  df-ima 4384  df-ec 6174 This theorem is referenced by:  qsid  6237
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