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Theorem imaexd 7928
Description: The image of a set is a set. Deduction version of imaexg 7925. (Contributed by Thierry Arnoux, 14-Feb-2025.)
Hypothesis
Ref Expression
rnexd.1 (𝜑𝐴𝑉)
Assertion
Ref Expression
imaexd (𝜑 → (𝐴𝐵) ∈ V)

Proof of Theorem imaexd
StepHypRef Expression
1 rnexd.1 . 2 (𝜑𝐴𝑉)
2 imaexg 7925 . 2 (𝐴𝑉 → (𝐴𝐵) ∈ V)
31, 2syl 17 1 (𝜑 → (𝐴𝐵) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  Vcvv 3471  cima 5683
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2698  ax-sep 5301  ax-nul 5308  ax-pr 5431  ax-un 7744
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2705  df-cleq 2719  df-clel 2805  df-ral 3058  df-rex 3067  df-rab 3429  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4325  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4911  df-br 5151  df-opab 5213  df-xp 5686  df-cnv 5688  df-dm 5690  df-rn 5691  df-res 5692  df-ima 5693
This theorem is referenced by:  mptcnfimad  7994  ghmquskerlem1  19239  ghmquskerco  19240  ghmquskerlem3  19242  ghmqusker  19243  ghmqusnsglem1  33147  ghmqusnsg  33149  algextdeglem4  33393  aks6d1c2lem4  41602  aks6d1c2  41605  aks6d1c6lem2  41647  aks6d1c6lem3  41648  aks6d1c7lem1  41656  aks6d1c7lem2  41657  isuspgrim0lem  47220
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