Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > elssuni | Unicode version |
Description: An element of a class is a subclass of its union. Theorem 8.6 of [Quine] p. 54. Also the basis for Proposition 7.20 of [TakeutiZaring] p. 40. (Contributed by NM, 6-Jun-1994.) |
Ref | Expression |
---|---|
elssuni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid 3117 | . 2 | |
2 | ssuni 3758 | . 2 | |
3 | 1, 2 | mpan 420 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 wss 3071 cuni 3736 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-in 3077 df-ss 3084 df-uni 3737 |
This theorem is referenced by: unissel 3765 ssunieq 3769 pwuni 4116 pwel 4140 uniopel 4178 iunpw 4401 dmrnssfld 4802 fvssunirng 5436 relfvssunirn 5437 sefvex 5442 riotaexg 5734 pwuninel2 6179 tfrlem9 6216 tfrexlem 6231 sbthlem1 6845 sbthlem2 6846 unirnioo 9756 eltopss 12176 toponss 12193 isbasis3g 12213 baspartn 12217 bastg 12230 tgcl 12233 epttop 12259 difopn 12277 ssntr 12291 isopn3 12294 isopn3i 12304 neiuni 12330 resttopon 12340 restopn2 12352 ssidcn 12379 lmtopcnp 12419 txuni2 12425 hmeoimaf1o 12483 tgioo 12715 bj-elssuniab 12998 |
Copyright terms: Public domain | W3C validator |