Theorem imaexi 43144

Description: The image of a set is a set. (Contributed by Glauco Siliprandi, 26-Jun-2021.)

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	. 2 ⊢ 𝐴 ∈ 𝑉
2		imaexg 7842	. 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴 “ 𝐵) ∈ V)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 “ 𝐵) ∈ V

Syntax hints:   ∈ wcel 2106  Vcvv 3443   “ cima 5633

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2708  ax-sep 5254  ax-nul 5261  ax-pr 5382  ax-un 7662

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2715  df-cleq 2729  df-clel 2815  df-ral 3063  df-rex 3072  df-rab 3406  df-v 3445  df-dif 3911  df-un 3913  df-in 3915  df-ss 3925  df-nul 4281  df-if 4485  df-sn 4585  df-pr 4587  df-op 4591  df-uni 4864  df-br 5104  df-opab 5166  df-xp 5636  df-cnv 5638  df-dm 5640  df-rn 5641  df-res 5642  df-ima 5643

This theorem is referenced by:  smfpimbor1lem1  44729