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Mirrors > Home > ILE Home > Th. List > sstpr | Unicode version |
Description: The subsets of a triple. (Contributed by Jim Kingdon, 11-Aug-2018.) |
Ref | Expression |
---|---|
sstpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssprr 3721 | . . 3 | |
2 | prsstp12 3711 | . . 3 | |
3 | 1, 2 | sstrdi 3140 | . 2 |
4 | snsstp3 3710 | . . . . 5 | |
5 | sseq1 3151 | . . . . 5 | |
6 | 4, 5 | mpbiri 167 | . . . 4 |
7 | prsstp13 3712 | . . . . 5 | |
8 | sseq1 3151 | . . . . 5 | |
9 | 7, 8 | mpbiri 167 | . . . 4 |
10 | 6, 9 | jaoi 706 | . . 3 |
11 | prsstp23 3713 | . . . . 5 | |
12 | sseq1 3151 | . . . . 5 | |
13 | 11, 12 | mpbiri 167 | . . . 4 |
14 | eqimss 3182 | . . . 4 | |
15 | 13, 14 | jaoi 706 | . . 3 |
16 | 10, 15 | jaoi 706 | . 2 |
17 | 3, 16 | jaoi 706 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 698 wceq 1335 wss 3102 c0 3395 csn 3561 cpr 3562 ctp 3563 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3396 df-sn 3567 df-pr 3568 df-tp 3569 |
This theorem is referenced by: pwtpss 3771 |
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