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Theorem eceq2 5963
 Description: Equality theorem for equivalence class. (Contributed by set.mm contributors, 23-Jul-1995.)
Assertion
Ref Expression
eceq2 (A = B → [C]A = [C]B)

Proof of Theorem eceq2
StepHypRef Expression
1 imaeq1 4937 . 2 (A = B → (A “ {C}) = (B “ {C}))
2 df-ec 5947 . 2 [C]A = (A “ {C})
3 df-ec 5947 . 2 [C]B = (B “ {C})
41, 2, 33eqtr4g 2410 1 (A = B → [C]A = [C]B)
 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-rex 2620  df-br 4640  df-ima 4727  df-ec 5947 This theorem is referenced by:  qseq2  5975
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