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Theorem imaeq2 4938
 Description: Equality theorem for image. (Contributed by set.mm contributors, 14-Aug-1994.)
Assertion
Ref Expression
imaeq2 (A = B → (CA) = (CB))

Proof of Theorem imaeq2
Dummy variables x y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 rexeq 2808 . . 3 (A = B → (y A yCxy B yCx))
21abbidv 2467 . 2 (A = B → {x y A yCx} = {x y B yCx})
3 df-ima 4727 . 2 (CA) = {x y A yCx}
4 df-ima 4727 . 2 (CB) = {x y B yCx}
52, 3, 43eqtr4g 2410 1 (A = B → (CA) = (CB))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  {cab 2339  ∃wrex 2615   class class class wbr 4639   “ cima 4722 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-ima 4727 This theorem is referenced by:  imaeq2i  4940  imaeq2d  4942  foima  5274  f1imacnv  5302  clos1induct  5880  ecexr  5950  ncdisjun  6136
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