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Mirrors > Home > ILE Home > Th. List > tpss | Unicode version |
Description: A triplet of elements of a class is a subset of the class. (Contributed by NM, 9-Apr-1994.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
tpss.1 | |
tpss.2 | |
tpss.3 |
Ref | Expression |
---|---|
tpss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unss 3117 | . 2 | |
2 | df-3an 887 | . . 3 | |
3 | tpss.1 | . . . . 5 | |
4 | tpss.2 | . . . . 5 | |
5 | 3, 4 | prss 3520 | . . . 4 |
6 | tpss.3 | . . . . 5 | |
7 | 6 | snss 3494 | . . . 4 |
8 | 5, 7 | anbi12i 433 | . . 3 |
9 | 2, 8 | bitri 173 | . 2 |
10 | df-tp 3383 | . . 3 | |
11 | 10 | sseq1i 2969 | . 2 |
12 | 1, 9, 11 | 3bitr4i 201 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 w3a 885 wcel 1393 cvv 2557 cun 2915 wss 2917 csn 3375 cpr 3376 ctp 3377 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-tp 3383 |
This theorem is referenced by: (None) |
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