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Theorem imaexi 45164
Description: The image of a set is a set. (Contributed by Glauco Siliprandi, 26-Jun-2021.) (Proof shortened by SN, 27-Apr-2025.)
Hypothesis
Ref Expression
imaexi.1 𝐴𝑉
Assertion
Ref Expression
imaexi (𝐴𝐵) ∈ V

Proof of Theorem imaexi
StepHypRef Expression
1 imaexi.1 . . 3 𝐴𝑉
21elexi 3501 . 2 𝐴 ∈ V
32imaex 7937 1 (𝐴𝐵) ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2106  Vcvv 3478  cima 5692
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pr 5438  ax-un 7754
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ral 3060  df-rex 3069  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-opab 5211  df-xp 5695  df-cnv 5697  df-dm 5699  df-rn 5700  df-res 5701  df-ima 5702
This theorem is referenced by:  smfpimbor1lem1  46754
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