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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 3732 | . . 3 | |
2 | elun 3259 | . . . 4 | |
3 | elun 3259 | . . . . . 6 | |
4 | vex 2725 | . . . . . . . 8 | |
5 | 4 | elpr 3592 | . . . . . . 7 |
6 | 4 | elpr 3592 | . . . . . . 7 |
7 | 5, 6 | orbi12i 754 | . . . . . 6 |
8 | 3, 7 | bitri 183 | . . . . 5 |
9 | elun 3259 | . . . . . 6 | |
10 | 4 | elpr 3592 | . . . . . . 7 |
11 | 4 | elpr 3592 | . . . . . . 7 |
12 | 10, 11 | orbi12i 754 | . . . . . 6 |
13 | 9, 12 | bitri 183 | . . . . 5 |
14 | 8, 13 | orbi12i 754 | . . . 4 |
15 | 2, 14 | bitri 183 | . . 3 |
16 | 4 | elpw 3560 | . . 3 |
17 | 1, 15, 16 | 3imtr4i 200 | . 2 |
18 | 17 | ssriv 3142 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 698 wceq 1342 wcel 2135 cun 3110 wss 3112 c0 3405 cpw 3554 csn 3571 cpr 3572 ctp 3573 |
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 604 ax-in2 605 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-3or 968 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2724 df-dif 3114 df-un 3116 df-in 3118 df-ss 3125 df-nul 3406 df-pw 3556 df-sn 3577 df-pr 3578 df-tp 3579 |
This theorem is referenced by: (None) |
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