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Mirrors > Home > MPE Home > Th. List > imaex | Structured version Visualization version GIF version |
Description: The image of a set is a set. Theorem 3.17 of [Monk1] p. 39. (Contributed by JJ, 24-Sep-2021.) |
Ref | Expression |
---|---|
imaex.1 | ⊢ 𝐴 ∈ V |
Ref | Expression |
---|---|
imaex | ⊢ (𝐴 “ 𝐵) ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imaex.1 | . 2 ⊢ 𝐴 ∈ V | |
2 | imaexg 7762 | . 2 ⊢ (𝐴 ∈ V → (𝐴 “ 𝐵) ∈ V) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐴 “ 𝐵) ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2106 Vcvv 3432 “ cima 5592 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2709 ax-sep 5223 ax-nul 5230 ax-pr 5352 ax-un 7588 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-3an 1088 df-tru 1542 df-fal 1552 df-ex 1783 df-sb 2068 df-clab 2716 df-cleq 2730 df-clel 2816 df-ral 3069 df-rex 3070 df-rab 3073 df-v 3434 df-dif 3890 df-un 3892 df-in 3894 df-ss 3904 df-nul 4257 df-if 4460 df-sn 4562 df-pr 4564 df-op 4568 df-uni 4840 df-br 5075 df-opab 5137 df-xp 5595 df-cnv 5597 df-dm 5599 df-rn 5600 df-res 5601 df-ima 5602 |
This theorem is referenced by: frxp 7967 pw2f1o 8864 ssenen 8938 fiint 9091 fissuni 9124 fipreima 9125 marypha1lem 9192 infxpenlem 9769 ackbij2lem2 9996 enfin2i 10077 fin1a2lem7 10162 fpwwe 10402 canthwelem 10406 tskuni 10539 isacs4lem 18262 gicsubgen 18894 gsumzaddlem 19522 isunit 19899 evpmss 20791 psgnevpmb 20792 ptbasfi 22732 hmphdis 22947 ustuqtop0 23392 utopsnneiplem 23399 neipcfilu 23448 nghmfval 23886 qtopbaslem 23922 fta1glem2 25331 fta1blem 25333 lgsqrlem4 26497 legval 26945 evpmval 31412 altgnsg 31416 elrspunidl 31606 zarcmplem 31831 frxp2 33791 frxp3 33797 brapply 34240 dfrdg4 34253 ptrest 35776 intima0 41256 elintima 41261 brtrclfv2 41335 |
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