Theorem imaexi 45920

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 3477	. 2 ⊢ 𝐴 ∈ V
3	2	imaex 7912	1 ⊢ (𝐴 “ 𝐵) ∈ V

Syntax hints:   ∈ wcel 2143  Vcvv 3455   “ cima 5666

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735  ax-sep 5258  ax-pr 5406  ax-un 7734

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-ral 3080  df-rex 3090  df-rab 3417  df-v 3457  df-dif 3909  df-un 3911  df-in 3913  df-ss 3923  df-nul 4288  df-if 4489  df-sn 4591  df-pr 4593  df-op 4597  df-uni 4874  df-br 5111  df-opab 5175  df-xp 5669  df-cnv 5671  df-dm 5673  df-rn 5674  df-res 5675  df-ima 5676

This theorem is referenced by:  smfpimbor1lem1  47495