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Theorem opkelimagek 4272
 Description: Membership in the Kuratowski image functor. (Contributed by SF, 20-Jan-2015.)
Hypotheses
Ref Expression
opkelimagek.1
opkelimagek.2
Assertion
Ref Expression
opkelimagek Imagek k

Proof of Theorem opkelimagek
StepHypRef Expression
1 opkelimagek.1 . 2
2 opkelimagek.2 . 2
3 opkelimagekg 4271 . 2 Imagek k
41, 2, 3mp2an 653 1 Imagek k
 Colors of variables: wff setvar class Syntax hints:   wb 176   wceq 1642   wcel 1710  cvv 2859  copk 4057  kcimak 4179  Imagekcimagek 4182 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  ax-nin 4078  ax-sn 4087 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-ne 2518  df-ral 2619  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-symdif 3216  df-ss 3259  df-nul 3551  df-pw 3724  df-sn 3741  df-pr 3742  df-opk 4058  df-1c 4136  df-pw1 4137  df-xpk 4185  df-cnvk 4186  df-ins2k 4187  df-ins3k 4188  df-imak 4189  df-cok 4190  df-sik 4192  df-ssetk 4193  df-imagek 4194 This theorem is referenced by:  preaddccan2lem1  4454  ltfinex  4464  evenodddisjlem1  4515  dfphi2  4569  dfop2lem1  4573  dfop2  4575  dfproj12  4576  phialllem1  4616  setconslem1  4731  setconslem2  4732  dfswap2  4741
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