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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.) |
Ref | Expression |
---|---|
vuniex | ⊢ ∪ 𝑥 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3176 | . 2 ⊢ 𝑥 ∈ V | |
2 | 1 | uniex 6851 | 1 ⊢ ∪ 𝑥 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1977 Vcvv 3173 ∪ cuni 4372 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-8 1979 ax-9 1986 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-sep 4709 ax-un 6847 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-rex 2902 df-v 3175 df-uni 4373 |
This theorem is referenced by: uniexg 6853 uniuni 6865 rankuni 8609 r0weon 8718 dfac3 8827 dfac5lem4 8832 dfac8 8840 dfacacn 8846 kmlem2 8856 cfslb2n 8973 ttukeylem5 9218 ttukeylem6 9219 brdom7disj 9234 brdom6disj 9235 intwun 9436 wunex2 9439 fnmrc 16090 mrcfval 16091 mrisval 16113 sylow2a 17857 distop 20610 fctop 20618 cctop 20620 ppttop 20621 epttop 20623 fncld 20636 mretopd 20706 toponmre 20707 iscnp2 20853 2ndcsep 21072 kgenf 21154 alexsubALTlem2 21662 pwsiga 29520 sigainb 29526 dmsigagen 29534 pwldsys 29547 ldsysgenld 29550 ldgenpisyslem1 29553 ddemeas 29626 brapply 31215 dfrdg4 31228 fnessref 31522 neibastop1 31524 bj-toprntopon 32244 finxpreclem2 32403 mbfresfi 32626 pwinfi 36888 pwsal 39211 intsal 39224 salexct 39228 0ome 39419 |
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