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Mirrors > Home > ILE Home > Th. List > ssequn2 | Unicode version |
Description: A relationship between subclass and union. (Contributed by NM, 13-Jun-1994.) |
Ref | Expression |
---|---|
ssequn2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssequn1 3287 | . 2 | |
2 | uncom 3261 | . . 3 | |
3 | 2 | eqeq1i 2172 | . 2 |
4 | 1, 3 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1342 cun 3109 wss 3111 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 |
This theorem is referenced by: unabs 3348 pwssunim 4256 pwundifss 4257 oneluni 4403 relresfld 5127 relcoi1 5129 fsnunf 5679 unsnfidcel 6877 fidcenumlemr 6911 exmidfodomrlemim 7148 ennnfonelemhf1o 12289 |
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