![]() |
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 3190 |
. 2
![]() ![]() ![]() ![]() | |
2 | ssuni 3846 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | mpan 424 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-in 3150 df-ss 3157 df-uni 3825 |
This theorem is referenced by: unissel 3853 ssunieq 3857 pwuni 4207 pwel 4233 uniopel 4271 iunpw 4495 dmrnssfld 4905 iotaexab 5211 fvssunirng 5546 relfvssunirn 5547 sefvex 5552 riotaexg 5852 pwuninel2 6302 tfrlem9 6339 tfrexlem 6354 sbthlem1 6981 sbthlem2 6982 unirnioo 9998 eltopss 13946 toponss 13963 isbasis3g 13983 baspartn 13987 bastg 13998 tgcl 14001 epttop 14027 difopn 14045 ssntr 14059 isopn3 14062 isopn3i 14072 neiuni 14098 resttopon 14108 restopn2 14120 ssidcn 14147 lmtopcnp 14187 txuni2 14193 hmeoimaf1o 14251 tgioo 14483 bj-elssuniab 14981 |
Copyright terms: Public domain | W3C validator |