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Mirrors > Home > ILE Home > Th. List > tpid3 | Unicode version |
Description: One of the three elements of an unordered triple. (Contributed by NM, 7-Apr-1994.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
tpid3.1 |
Ref | Expression |
---|---|
tpid3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2137 | . . 3 | |
2 | 1 | 3mix3i 1155 | . 2 |
3 | tpid3.1 | . . 3 | |
4 | 3 | eltp 3566 | . 2 |
5 | 2, 4 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: w3o 961 wceq 1331 wcel 1480 cvv 2681 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-3or 963 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-sn 3528 df-pr 3529 df-tp 3530 |
This theorem is referenced by: (None) |
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