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Theorem imakeq2 4225
 Description: Equality theorem for Kuratowski image. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
imakeq2 (A = B → (Ck A) = (Ck B))

Proof of Theorem imakeq2
Dummy variables x y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 rexeq 2808 . . 3 (A = B → (y Ay, x Cy By, x C))
21abbidv 2467 . 2 (A = B → {x y Ay, x C} = {x y By, x C})
3 df-imak 4189 . 2 (Ck A) = {x y Ay, x C}
4 df-imak 4189 . 2 (Ck B) = {x y By, x C}
52, 3, 43eqtr4g 2410 1 (A = B → (Ck A) = (Ck B))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   ∈ wcel 1710  {cab 2339  ∃wrex 2615  ⟪copk 4057   “k cimak 4179 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-imak 4189 This theorem is referenced by:  imakeq2i  4227  imakeq2d  4229  addceq1  4383  phieq  4570  opeq1  4578  opeq2  4579  proj1eq  4589  proj2eq  4590
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