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Mirrors > Home > ILE Home > Th. List > pwtpss | Unicode version |
Description: The power set of an unordered triple. (Contributed by Jim Kingdon, 13-Aug-2018.) |
Ref | Expression |
---|---|
pwtpss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sstpr 3549 | . . 3 | |
2 | elun 3113 | . . . 4 | |
3 | elun 3113 | . . . . . 6 | |
4 | vex 2604 | . . . . . . . 8 | |
5 | 4 | elpr 3419 | . . . . . . 7 |
6 | 4 | elpr 3419 | . . . . . . 7 |
7 | 5, 6 | orbi12i 713 | . . . . . 6 |
8 | 3, 7 | bitri 182 | . . . . 5 |
9 | elun 3113 | . . . . . 6 | |
10 | 4 | elpr 3419 | . . . . . . 7 |
11 | 4 | elpr 3419 | . . . . . . 7 |
12 | 10, 11 | orbi12i 713 | . . . . . 6 |
13 | 9, 12 | bitri 182 | . . . . 5 |
14 | 8, 13 | orbi12i 713 | . . . 4 |
15 | 2, 14 | bitri 182 | . . 3 |
16 | 4 | elpw 3388 | . . 3 |
17 | 1, 15, 16 | 3imtr4i 199 | . 2 |
18 | 17 | ssriv 3003 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 661 wceq 1284 wcel 1433 cun 2971 wss 2973 c0 3251 cpw 3382 csn 3398 cpr 3399 ctp 3400 |
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-in1 576 ax-in2 577 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-3or 920 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-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-nul 3252 df-pw 3384 df-sn 3404 df-pr 3405 df-tp 3406 |
This theorem is referenced by: (None) |
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