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| Description: The image of a set is a set. Deduction version of imaexg 7936. (Contributed by Thierry Arnoux, 14-Feb-2025.) | 
| Ref | Expression | 
|---|---|
| rnexd.1 | ⊢ (𝜑 → 𝐴 ∈ 𝑉) | 
| Ref | Expression | 
|---|---|
| imaexd | ⊢ (𝜑 → (𝐴 “ 𝐵) ∈ V) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | rnexd.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ 𝑉) | |
| 2 | imaexg 7936 | . 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴 “ 𝐵) ∈ V) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐴 “ 𝐵) ∈ V) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∈ wcel 2107 Vcvv 3479 “ cima 5687 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-ext 2707 ax-sep 5295 ax-nul 5305 ax-pr 5431 ax-un 7756 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1542 df-fal 1552 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-ral 3061 df-rex 3070 df-rab 3436 df-v 3481 df-dif 3953 df-un 3955 df-in 3957 df-ss 3967 df-nul 4333 df-if 4525 df-sn 4626 df-pr 4628 df-op 4632 df-uni 4907 df-br 5143 df-opab 5205 df-xp 5690 df-cnv 5692 df-dm 5694 df-rn 5695 df-res 5696 df-ima 5697 | 
| This theorem is referenced by: mptcnfimad 8012 ghmqusnsglem1 19299 ghmqusnsg 19301 ghmquskerlem1 19302 ghmquskerco 19303 ghmquskerlem3 19305 ghmqusker 19306 gsumfs2d 33059 algextdeglem4 33762 aks6d1c2lem4 42129 aks6d1c2 42132 aks6d1c6lem2 42173 aks6d1c6lem3 42174 aks6d1c7lem1 42182 aks6d1c7lem2 42183 sge0f1o 46402 isuspgrim0lem 47876 isubgr3stgrlem5 47942 | 
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