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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 7103 | . 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 1990 Vcvv 3200 “ cima 5117 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-xp 5120 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 |
This theorem is referenced by: frxp 7287 pw2f1o 8065 ssenen 8134 fiint 8237 fissuni 8271 fipreima 8272 marypha1lem 8339 infxpenlem 8836 ackbij2lem2 9062 enfin2i 9143 fin1a2lem7 9228 fpwwe 9468 canthwelem 9472 tskuni 9605 isacs4lem 17168 gicsubgen 17721 gsumzaddlem 18321 isunit 18657 evpmss 19932 psgnevpmb 19933 ptbasfi 21384 hmphdis 21599 ustuqtop0 22044 utopsnneiplem 22051 neipcfilu 22100 nghmfval 22526 fta1glem2 23926 fta1blem 23928 lgsqrlem4 25074 legval 25479 |
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