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Mirrors > Home > MPE Home > Th. List > imaexd | Structured version Visualization version GIF version |
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 2106 Vcvv 3478 “ cima 5692 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 ax-sep 5302 ax-nul 5312 ax-pr 5438 ax-un 7754 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1540 df-fal 1550 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-ral 3060 df-rex 3069 df-rab 3434 df-v 3480 df-dif 3966 df-un 3968 df-in 3970 df-ss 3980 df-nul 4340 df-if 4532 df-sn 4632 df-pr 4634 df-op 4638 df-uni 4913 df-br 5149 df-opab 5211 df-xp 5695 df-cnv 5697 df-dm 5699 df-rn 5700 df-res 5701 df-ima 5702 |
This theorem is referenced by: mptcnfimad 8010 ghmqusnsglem1 19311 ghmqusnsg 19313 ghmquskerlem1 19314 ghmquskerco 19315 ghmquskerlem3 19317 ghmqusker 19318 gsumfs2d 33041 algextdeglem4 33726 aks6d1c2lem4 42109 aks6d1c2 42112 aks6d1c6lem2 42153 aks6d1c6lem3 42154 aks6d1c7lem1 42162 aks6d1c7lem2 42163 sge0f1o 46338 isuspgrim0lem 47809 isubgr3stgrlem5 47873 |
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