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Theorem eceq2 6275
Description: Equality theorem for equivalence class. (Contributed by NM, 23-Jul-1995.)
Assertion
Ref Expression
eceq2  |-  ( A  =  B  ->  [ C ] A  =  [ C ] B )

Proof of Theorem eceq2
StepHypRef Expression
1 imaeq1 4733 . 2  |-  ( A  =  B  ->  ( A " { C }
)  =  ( B
" { C }
) )
2 df-ec 6240 . 2  |-  [ C ] A  =  ( A " { C }
)
3 df-ec 6240 . 2  |-  [ C ] B  =  ( B " { C }
)
41, 2, 33eqtr4g 2142 1  |-  ( A  =  B  ->  [ C ] A  =  [ C ] B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1287   {csn 3431   "cima 4413   [cec 6236
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617  df-un 2992  df-in 2994  df-ss 3001  df-sn 3437  df-pr 3438  df-op 3440  df-br 3821  df-opab 3875  df-cnv 4418  df-dm 4420  df-rn 4421  df-res 4422  df-ima 4423  df-ec 6240
This theorem is referenced by:  qseq2  6287  nqnq0pi  6934
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