Theorem imaexi 46507

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 3476	. 2 ⊢ 𝐴 ∈ V
3	2	imaex 7960	1 ⊢ (𝐴 “ 𝐵) ∈ V

This proof depends on syntax axioms:   ∈ wcel 2147  Vcvv 3454   “ cima 5661

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-sep 5255  ax-pr 5398  ax-un 7783

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-v 3456  df-ss 3901  df-dif 4050  df-in 4094  df-un 4154  df-nul 4282  df-if 4486  df-sn 4589  df-pr 4591  df-op 4841  df-uni 4873  df-br 5109  df-opab 5174  df-xp 5664  df-rel 5665  df-cnv 5666  df-dm 5668  df-rn 5669  df-res 5670  df-ima 5671

This theorem is used by:  smfpimbor1lem1  48081