Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 3245 | . 2 | |
2 | df-3an 964 | . . 3 | |
3 | tpss.1 | . . . . 5 | |
4 | tpss.2 | . . . . 5 | |
5 | 3, 4 | prss 3671 | . . . 4 |
6 | tpss.3 | . . . . 5 | |
7 | 6 | snss 3644 | . . . 4 |
8 | 5, 7 | anbi12i 455 | . . 3 |
9 | 2, 8 | bitri 183 | . 2 |
10 | df-tp 3530 | . . 3 | |
11 | 10 | sseq1i 3118 | . 2 |
12 | 1, 9, 11 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 w3a 962 wcel 1480 cvv 2681 cun 3064 wss 3066 csn 3522 cpr 3523 ctp 3524 |
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-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 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-pr 3529 df-tp 3530 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |