Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > eqrelrel | Unicode version |
Description: Extensionality principle for ordered triples, analogous to eqrel 4623. Use relrelss 5060 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 3245 | . 2 | |
2 | ssrelrel 4634 | . . . 4 | |
3 | ssrelrel 4634 | . . . 4 | |
4 | 2, 3 | bi2anan9 595 | . . 3 |
5 | eqss 3107 | . . 3 | |
6 | 2albiim 1464 | . . . . 5 | |
7 | 6 | albii 1446 | . . . 4 |
8 | 19.26 1457 | . . . 4 | |
9 | 7, 8 | bitri 183 | . . 3 |
10 | 4, 5, 9 | 3bitr4g 222 | . 2 |
11 | 1, 10 | sylbir 134 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wceq 1331 wcel 1480 cvv 2681 cun 3064 wss 3066 cop 3525 cxp 4532 |
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-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
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-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-opab 3985 df-xp 4540 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |