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Theorem imakeq1d 4228
 Description: Equality theorem for Kuratowski image. (Contributed by SF, 12-Jan-2015.)
Hypothesis
Ref Expression
imakeq1d.1 (φA = B)
Assertion
Ref Expression
imakeq1d (φ → (Ak C) = (Bk C))

Proof of Theorem imakeq1d
StepHypRef Expression
1 imakeq1d.1 . 2 (φA = B)
2 imakeq1 4224 . 2 (A = B → (Ak C) = (Bk C))
31, 2syl 15 1 (φ → (Ak C) = (Bk C))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   “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-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-imak 4189 This theorem is referenced by:  cokeq1  4230  cokeq2  4231  imagekeq  4244  addceq2  4384
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