Mathbox for Glauco Siliprandi < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  imaexi Structured version   Visualization version   GIF version

Theorem imaexi 39231
 Description: The image of a set is a set. (Contributed by Glauco Siliprandi, 26-Jun-2021.)
Hypothesis
Ref Expression
imaexi.1 𝐴𝑉
Assertion
Ref Expression
imaexi (𝐴𝐵) ∈ V

Proof of Theorem imaexi
StepHypRef Expression
1 imaexi.1 . 2 𝐴𝑉
2 imaexg 7088 . 2 (𝐴𝑉 → (𝐴𝐵) ∈ V)
31, 2ax-mp 5 1 (𝐴𝐵) ∈ V
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1988  Vcvv 3195   “ cima 5107 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-8 1990  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600  ax-sep 4772  ax-nul 4780  ax-pr 4897  ax-un 6934 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-eu 2472  df-mo 2473  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-ral 2914  df-rex 2915  df-rab 2918  df-v 3197  df-dif 3570  df-un 3572  df-in 3574  df-ss 3581  df-nul 3908  df-if 4078  df-sn 4169  df-pr 4171  df-op 4175  df-uni 4428  df-br 4645  df-opab 4704  df-xp 5110  df-cnv 5112  df-dm 5114  df-rn 5115  df-res 5116  df-ima 5117 This theorem is referenced by:  smfpimbor1lem1  40768
 Copyright terms: Public domain W3C validator