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Theorem cokeq12d 4237
 Description: Equality deduction for Kuratowski composition of two classes. (Contributed by SF, 12-Jan-2015.)
Hypotheses
Ref Expression
cokeq12d.1 (φA = B)
cokeq12d.2 (φC = D)
Assertion
Ref Expression
cokeq12d (φ → (A k C) = (B k D))

Proof of Theorem cokeq12d
StepHypRef Expression
1 cokeq12d.1 . . 3 (φA = B)
21cokeq1d 4234 . 2 (φ → (A k C) = (B k C))
3 cokeq12d.2 . . 3 (φC = D)
43cokeq2d 4235 . 2 (φ → (B k C) = (B k D))
52, 4eqtrd 2385 1 (φ → (A k C) = (B k D))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   ∘k ccomk 4180 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-3an 936  df-nan 1288  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-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-cnvk 4186  df-ins2k 4187  df-ins3k 4188  df-imak 4189  df-cok 4190 This theorem is referenced by: (None)
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