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Theorem eceq1 5962
Description: Equality theorem for equivalence class. (Contributed by set.mm contributors, 23-Jul-1995.)
Assertion
Ref Expression
eceq1

Proof of Theorem eceq1
StepHypRef Expression
1 sneq 3744 . . 3
21imaeq2d 4942 . 2
3 df-ec 5947 . 2
4 df-ec 5947 . 2
52, 3, 43eqtr4g 2410 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wceq 1642  csn 3737  cima 4722  cec 5945
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-sn 3741  df-ima 4727  df-ec 5947
This theorem is referenced by:  ecelqsg  5979  snec  5987  ecoptocl  5996  nceq  6108
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