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| Mirrors > Home > MPE Home > Th. List > vuniex | Structured version Visualization version GIF version | ||
| Description: The union of a setvar is a set. (Contributed by BJ, 3-May-2021.) (Revised by BJ, 6-Apr-2024.) |
| Ref | Expression |
|---|---|
| vuniex | ⊢ ∪ 𝑥 ∈ V |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | uniex2 7758 | . 2 ⊢ ∃𝑦 𝑦 = ∪ 𝑥 | |
| 2 | 1 | issetri 3499 | 1 ⊢ ∪ 𝑥 ∈ V |
| Colors of variables: wff setvar class |
| Syntax hints: ∈ wcel 2108 Vcvv 3480 ∪ cuni 4907 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 ax-sep 5296 ax-un 7755 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-uni 4908 |
| This theorem is referenced by: uniexg 7760 uniuni 7782 rankuni 9903 r0weon 10052 dfac3 10161 dfac5lem4 10166 dfac5lem4OLD 10168 dfac8 10176 dfacacn 10182 kmlem2 10192 cfslb2n 10308 ttukeylem5 10553 ttukeylem6 10554 brdom7disj 10571 brdom6disj 10572 intwun 10775 wunex2 10778 fnmrc 17650 mrcfval 17651 mrisval 17673 sylow2a 19637 toprntopon 22931 distop 23002 fctop 23011 cctop 23013 ppttop 23014 epttop 23016 fncld 23030 mretopd 23100 toponmre 23101 iscnp2 23247 2ndcsep 23467 kgenf 23549 alexsubALTlem2 24056 pwsiga 34131 sigainb 34137 dmsigagen 34145 pwldsys 34158 ldsysgenld 34161 ldgenpisyslem1 34164 ddemeas 34237 brapply 35939 dfrdg4 35952 fnessref 36358 neibastop1 36360 finxpreclem2 37391 mbfresfi 37673 pwinfi 43577 pwsal 46330 intsal 46345 salexct 46349 0ome 46544 |
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