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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 7728 | . 2 ⊢ ∃𝑦 𝑦 = ∪ 𝑥 | |
2 | 1 | issetri 3491 | 1 ⊢ ∪ 𝑥 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2107 Vcvv 3475 ∪ cuni 4909 |
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 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 ax-sep 5300 ax-un 7725 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-v 3477 df-uni 4910 |
This theorem is referenced by: uniexg 7730 uniuni 7749 rankuni 9858 r0weon 10007 dfac3 10116 dfac5lem4 10121 dfac8 10130 dfacacn 10136 kmlem2 10146 cfslb2n 10263 ttukeylem5 10508 ttukeylem6 10509 brdom7disj 10526 brdom6disj 10527 intwun 10730 wunex2 10733 fnmrc 17551 mrcfval 17552 mrisval 17574 sylow2a 19487 toprntopon 22427 distop 22498 fctop 22507 cctop 22509 ppttop 22510 epttop 22512 fncld 22526 mretopd 22596 toponmre 22597 iscnp2 22743 2ndcsep 22963 kgenf 23045 alexsubALTlem2 23552 pwsiga 33128 sigainb 33134 dmsigagen 33142 pwldsys 33155 ldsysgenld 33158 ldgenpisyslem1 33161 ddemeas 33234 brapply 34910 dfrdg4 34923 fnessref 35242 neibastop1 35244 finxpreclem2 36271 mbfresfi 36534 pwinfi 42315 pwsal 45031 intsal 45046 salexct 45050 0ome 45245 |
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