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Theorem elimakvg 4258
 Description: Membership in a Kuratowski image under V. (Contributed by SF, 13-Jan-2015.)
Assertion
Ref Expression
elimakvg (C V → (C (Ak V) ↔ yy, C A))
Distinct variable groups:   y,A   y,C
Allowed substitution hint:   V(y)

Proof of Theorem elimakvg
StepHypRef Expression
1 elimakg 4257 . 2 (C V → (C (Ak V) ↔ y V ⟪y, C A))
2 rexv 2873 . 2 (y V ⟪y, C Ayy, C A)
31, 2syl6bb 252 1 (C V → (C (Ak V) ↔ yy, C A))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∃wex 1541   ∈ wcel 1710  ∃wrex 2615  Vcvv 2859  ⟪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-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-un 3214  df-sn 3741  df-pr 3742  df-opk 4058  df-imak 4189 This theorem is referenced by:  elimakv  4260
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