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Theorem imaex 7339
Description: The image of a set is a set. Theorem 3.17 of [Monk1] p. 39. (Contributed by JJ, 24-Sep-2021.)
Hypothesis
Ref Expression
imaex.1 𝐴 ∈ V
Assertion
Ref Expression
imaex (𝐴𝐵) ∈ V

Proof of Theorem imaex
StepHypRef Expression
1 imaex.1 . 2 𝐴 ∈ V
2 imaexg 7338 . 2 (𝐴 ∈ V → (𝐴𝐵) ∈ V)
31, 2ax-mp 5 1 (𝐴𝐵) ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2157  Vcvv 3385  cima 5315
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-8 2159  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2377  ax-ext 2777  ax-sep 4975  ax-nul 4983  ax-pr 5097  ax-un 7183
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-3an 1110  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-mo 2591  df-eu 2609  df-clab 2786  df-cleq 2792  df-clel 2795  df-nfc 2930  df-ral 3094  df-rex 3095  df-rab 3098  df-v 3387  df-dif 3772  df-un 3774  df-in 3776  df-ss 3783  df-nul 4116  df-if 4278  df-sn 4369  df-pr 4371  df-op 4375  df-uni 4629  df-br 4844  df-opab 4906  df-xp 5318  df-cnv 5320  df-dm 5322  df-rn 5323  df-res 5324  df-ima 5325
This theorem is referenced by:  frxp  7524  pw2f1o  8307  ssenen  8376  fiint  8479  fissuni  8513  fipreima  8514  marypha1lem  8581  infxpenlem  9122  ackbij2lem2  9350  enfin2i  9431  fin1a2lem7  9516  fpwwe  9756  canthwelem  9760  tskuni  9893  isacs4lem  17483  gicsubgen  18033  gsumzaddlem  18636  isunit  18973  evpmss  20253  psgnevpmb  20254  ptbasfi  21713  hmphdis  21928  ustuqtop0  22372  utopsnneiplem  22379  neipcfilu  22428  nghmfval  22854  fta1glem2  24267  fta1blem  24269  lgsqrlem4  25426  legval  25835  brapply  32558  dfrdg4  32571
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