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Mirrors > Home > ILE Home > Th. List > eqrelrel | Unicode version |
Description: Extensionality principle for ordered triples, analogous to eqrel 4447. Use relrelss 4864 to express the antecedent in terms of the relation predicate. (Contributed by NM, 17-Dec-2008.) |
Ref | Expression |
---|---|
eqrelrel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unss 3146 | . 2 | |
2 | ssrelrel 4458 | . . . 4 | |
3 | ssrelrel 4458 | . . . 4 | |
4 | 2, 3 | bi2anan9 570 | . . 3 |
5 | eqss 3014 | . . 3 | |
6 | 2albiim 1417 | . . . . 5 | |
7 | 6 | albii 1399 | . . . 4 |
8 | 19.26 1410 | . . . 4 | |
9 | 7, 8 | bitri 182 | . . 3 |
10 | 4, 5, 9 | 3bitr4g 221 | . 2 |
11 | 1, 10 | sylbir 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wceq 1284 wcel 1433 cvv 2601 cun 2971 wss 2973 cop 3401 cxp 4361 |
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-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 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-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-opab 3840 df-xp 4369 |
This theorem is referenced by: (None) |
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