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Mirrors > Home > ILE Home > Th. List > tpid1 | 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 |
---|---|
tpid1.1 |
Ref | Expression |
---|---|
tpid1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2081 | . . 3 | |
2 | 1 | 3mix1i 1110 | . 2 |
3 | tpid1.1 | . . 3 | |
4 | 3 | eltp 3440 | . 2 |
5 | 2, 4 | mpbir 144 | 1 |
Colors of variables: wff set class |
Syntax hints: w3o 918 wceq 1284 wcel 1433 cvv 2601 ctp 3400 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3or 920 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-un 2977 df-sn 3404 df-pr 3405 df-tp 3406 |
This theorem is referenced by: tpnz 3515 |
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