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Mirrors > Home > ILE Home > Th. List > pwunss | Unicode version |
Description: The power class of the union of two classes includes the union of their power classes. Exercise 4.12(k) of [Mendelson] p. 235. (Contributed by NM, 23-Nov-2003.) |
Ref | Expression |
---|---|
pwunss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssun 3151 | . . 3 | |
2 | elun 3113 | . . . 4 | |
3 | vex 2604 | . . . . . 6 | |
4 | 3 | elpw 3388 | . . . . 5 |
5 | 3 | elpw 3388 | . . . . 5 |
6 | 4, 5 | orbi12i 713 | . . . 4 |
7 | 2, 6 | bitri 182 | . . 3 |
8 | 3 | elpw 3388 | . . 3 |
9 | 1, 7, 8 | 3imtr4i 199 | . 2 |
10 | 9 | ssriv 3003 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 661 wcel 1433 cun 2971 wss 2973 cpw 3382 |
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 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 |
This theorem is referenced by: pwundifss 4040 pwunim 4041 |
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