Theorem imaexi 45576

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	⊢ 𝐴 ∈ 𝑉

Assertion

Ref	Expression
imaexi	⊢ (𝐴 “ 𝐵) ∈ V

Proof of Theorem imaexi

Step	Hyp	Ref	Expression
1		imaexi.1	. . 3 ⊢ 𝐴 ∈ 𝑉
2	1	elexi 3465	. 2 ⊢ 𝐴 ∈ V
3	2	imaex 7866	1 ⊢ (𝐴 “ 𝐵) ∈ V

Syntax hints:   ∈ wcel 2114  Vcvv 3442   “ cima 5635

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-sep 5243  ax-pr 5379  ax-un 7690

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-ral 3053  df-rex 3063  df-rab 3402  df-v 3444  df-dif 3906  df-un 3908  df-in 3910  df-ss 3920  df-nul 4288  df-if 4482  df-sn 4583  df-pr 4585  df-op 4589  df-uni 4866  df-br 5101  df-opab 5163  df-xp 5638  df-cnv 5640  df-dm 5642  df-rn 5643  df-res 5644  df-ima 5645

This theorem is referenced by:  smfpimbor1lem1  47153