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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 3684 | . . 3 | |
2 | elun 3217 | . . . 4 | |
3 | elun 3217 | . . . . . 6 | |
4 | vex 2689 | . . . . . . . 8 | |
5 | 4 | elpr 3548 | . . . . . . 7 |
6 | 4 | elpr 3548 | . . . . . . 7 |
7 | 5, 6 | orbi12i 753 | . . . . . 6 |
8 | 3, 7 | bitri 183 | . . . . 5 |
9 | elun 3217 | . . . . . 6 | |
10 | 4 | elpr 3548 | . . . . . . 7 |
11 | 4 | elpr 3548 | . . . . . . 7 |
12 | 10, 11 | orbi12i 753 | . . . . . 6 |
13 | 9, 12 | bitri 183 | . . . . 5 |
14 | 8, 13 | orbi12i 753 | . . . 4 |
15 | 2, 14 | bitri 183 | . . 3 |
16 | 4 | elpw 3516 | . . 3 |
17 | 1, 15, 16 | 3imtr4i 200 | . 2 |
18 | 17 | ssriv 3101 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 697 wceq 1331 wcel 1480 cun 3069 wss 3071 c0 3363 cpw 3510 csn 3527 cpr 3528 ctp 3529 |
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-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3or 963 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-pw 3512 df-sn 3533 df-pr 3534 df-tp 3535 |
This theorem is referenced by: (None) |
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