Theorem imaexd 7846

Description: The image of a set is a set. Deduction version of imaexg 7843. (Contributed by Thierry Arnoux, 14-Feb-2025.)

Hypothesis

Ref	Expression
rnexd.1	⊢ (𝜑 → 𝐴 ∈ 𝑉)

Assertion

Ref	Expression
imaexd	⊢ (𝜑 → (𝐴 “ 𝐵) ∈ V)

Proof of Theorem imaexd

Step	Hyp	Ref	Expression
1		rnexd.1	. 2 ⊢ (𝜑 → 𝐴 ∈ 𝑉)
2		imaexg 7843	. 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴 “ 𝐵) ∈ V)
3	1, 2	syl 17	1 ⊢ (𝜑 → (𝐴 “ 𝐵) ∈ V)

Syntax hints:   → wi 4   ∈ wcel 2111  Vcvv 3436   “ cima 5619

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703  ax-sep 5234  ax-nul 5244  ax-pr 5370  ax-un 7668

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-ral 3048  df-rex 3057  df-rab 3396  df-v 3438  df-dif 3905  df-un 3907  df-in 3909  df-ss 3919  df-nul 4284  df-if 4476  df-sn 4577  df-pr 4579  df-op 4583  df-uni 4860  df-br 5092  df-opab 5154  df-xp 5622  df-cnv 5624  df-dm 5626  df-rn 5627  df-res 5628  df-ima 5629

This theorem is referenced by:  mptcnfimad  7918  ghmqusnsglem1  19193  ghmqusnsg  19195  ghmquskerlem1  19196  ghmquskerco  19197  ghmquskerlem3  19199  ghmqusker  19200  gsumfs2d  33033  algextdeglem4  33731  aks6d1c2lem4  42166  aks6d1c2  42169  aks6d1c6lem2  42210  aks6d1c6lem3  42211  aks6d1c7lem1  42219  aks6d1c7lem2  42220  sge0f1o  46426  isuspgrim0lem  47930  isubgr3stgrlem5  48007  imasubclem1  49142