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Theorem imakex 4300
 Description: The image of a set under a set is a set. (Contributed by SF, 14-Jan-2015.)
Hypotheses
Ref Expression
imakex.1 A V
imakex.2 B V
Assertion
Ref Expression
imakex (Ak B) V

Proof of Theorem imakex
StepHypRef Expression
1 imakex.1 . 2 A V
2 imakex.2 . 2 B V
3 imakexg 4299 . 2 ((A V B V) → (Ak B) V)
41, 2, 3mp2an 653 1 (Ak B) V
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1710  Vcvv 2859   “k cimak 4179 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-xp 4079  ax-cnv 4080  ax-1c 4081  ax-si 4083  ax-typlower 4086  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-ss 3259  df-nul 3551  df-sn 3741  df-pr 3742  df-opk 4058  df-1c 4136  df-xpk 4185  df-cnvk 4186  df-imak 4189  df-p6 4191  df-sik 4192 This theorem is referenced by:  setswithex  4322  addcexlem  4382  nncex  4396  nnc0suc  4412  nncaddccl  4419  nnsucelrlem1  4424  nndisjeq  4429  preaddccan2lem1  4454  ltfinex  4464  ltfintrilem1  4465  ssfin  4470  ncfinraiselem2  4480  ncfinlowerlem1  4482  tfinrelkex  4487  evenfinex  4503  oddfinex  4504  evenodddisjlem1  4515  nnadjoinlem1  4519  nnpweqlem1  4522  srelkex  4525  sfintfinlem1  4531  tfinnnlem1  4533  spfinex  4537  vfinspss  4551  vfinspclt  4552  vfinncsp  4554  phiexg  4571  opexg  4587  proj1exg  4591  proj2exg  4592  phialllem1  4616  setconslem5  4735  1stex  4739  swapex  4742  ssetex  4744
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