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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid 3044 |
. 2
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2 | ssuni 3675 |
. 2
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3 | 1, 2 | mpan 415 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-v 2621 df-in 3005 df-ss 3012 df-uni 3654 |
This theorem is referenced by: unissel 3682 ssunieq 3686 pwuni 4027 pwel 4045 uniopel 4083 iunpw 4302 dmrnssfld 4696 fvssunirng 5320 relfvssunirn 5321 sefvex 5326 riotaexg 5612 pwuninel2 6047 tfrlem9 6084 tfrexlem 6099 sbthlem1 6666 sbthlem2 6667 unirnioo 9391 eltopss 11606 toponss 11622 bj-elssuniab 11691 |
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