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Mirrors > Home > ILE Home > Th. List > elco | Unicode version |
Description: Elements of a composed relation. (Contributed by BJ, 10-Jul-2022.) |
Ref | Expression |
---|---|
elco |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-co 4556 | . . 3 | |
2 | 1 | eleq2i 2207 | . 2 |
3 | elopab 4188 | . . 3 | |
4 | 19.42v 1879 | . . . . . . 7 | |
5 | 4 | bicomi 131 | . . . . . 6 |
6 | 5 | exbii 1585 | . . . . 5 |
7 | excom 1643 | . . . . 5 | |
8 | 6, 7 | bitri 183 | . . . 4 |
9 | 8 | exbii 1585 | . . 3 |
10 | 3, 9 | bitri 183 | . 2 |
11 | 2, 10 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1332 wex 1469 wcel 1481 cop 3535 class class class wbr 3937 copab 3996 ccom 4551 |
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 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-opab 3998 df-co 4556 |
This theorem is referenced by: (None) |
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