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Mirrors > Home > MPE Home > Th. List > vpwex | Structured version Visualization version GIF version |
Description: The powerset of a setvar is a set. (Contributed by BJ, 3-May-2021.) |
Ref | Expression |
---|---|
vpwex | ⊢ 𝒫 𝑥 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3203 | . 2 ⊢ 𝑥 ∈ V | |
2 | 1 | pwex 4848 | 1 ⊢ 𝒫 𝑥 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1990 Vcvv 3200 𝒫 cpw 4158 |
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-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-pow 4843 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-v 3202 df-in 3581 df-ss 3588 df-pw 4160 |
This theorem is referenced by: pwexg 4850 pwnex 6968 inf3lem7 8531 dfac8 8957 dfac13 8964 ackbij1lem5 9046 ackbij1lem8 9049 dominf 9267 numthcor 9316 dominfac 9395 intwun 9557 wunex2 9560 eltsk2g 9573 inttsk 9596 tskcard 9603 intgru 9636 gruina 9640 axgroth6 9650 ismre 16250 fnmre 16251 mreacs 16319 isacs5lem 17169 pmtrfval 17870 istopon 20717 dmtopon 20727 tgdom 20782 isfbas 21633 bj-snglex 32961 pwinfi 37869 ntrrn 38420 ntrf 38421 dssmapntrcls 38426 |
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