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Mirrors > Home > NFE 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 3437 | . 2 | |
2 | df-3an 936 | . . 3 | |
3 | tpss.1 | . . . . 5 | |
4 | tpss.2 | . . . . 5 | |
5 | 3, 4 | prss 3861 | . . . 4 |
6 | tpss.3 | . . . . 5 | |
7 | 6 | snss 3838 | . . . 4 |
8 | 5, 7 | anbi12i 678 | . . 3 |
9 | 2, 8 | bitri 240 | . 2 |
10 | df-tp 3743 | . . 3 | |
11 | 10 | sseq1i 3295 | . 2 |
12 | 1, 9, 11 | 3bitr4i 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wa 358 w3a 934 wcel 1710 cvv 2859 cun 3207 wss 3257 csn 3737 cpr 3738 ctp 3739 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-ss 3259 df-sn 3741 df-pr 3742 df-tp 3743 |
This theorem is referenced by: (None) |
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