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Mirrors > Home > ILE Home > Th. List > coiun | Unicode version |
Description: Composition with an indexed union. (Contributed by NM, 21-Dec-2008.) |
Ref | Expression |
---|---|
coiun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relco 5109 | . 2 | |
2 | reliun 4732 | . . 3 | |
3 | relco 5109 | . . . 4 | |
4 | 3 | a1i 9 | . . 3 |
5 | 2, 4 | mprgbir 2528 | . 2 |
6 | eliun 3877 | . . . . . . . 8 | |
7 | df-br 3990 | . . . . . . . 8 | |
8 | df-br 3990 | . . . . . . . . 9 | |
9 | 8 | rexbii 2477 | . . . . . . . 8 |
10 | 6, 7, 9 | 3bitr4i 211 | . . . . . . 7 |
11 | 10 | anbi1i 455 | . . . . . 6 |
12 | r19.41v 2626 | . . . . . 6 | |
13 | 11, 12 | bitr4i 186 | . . . . 5 |
14 | 13 | exbii 1598 | . . . 4 |
15 | rexcom4 2753 | . . . 4 | |
16 | 14, 15 | bitr4i 186 | . . 3 |
17 | vex 2733 | . . . 4 | |
18 | vex 2733 | . . . 4 | |
19 | 17, 18 | opelco 4783 | . . 3 |
20 | eliun 3877 | . . . 4 | |
21 | 17, 18 | opelco 4783 | . . . . 5 |
22 | 21 | rexbii 2477 | . . . 4 |
23 | 20, 22 | bitri 183 | . . 3 |
24 | 16, 19, 23 | 3bitr4i 211 | . 2 |
25 | 1, 5, 24 | eqrelriiv 4705 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 wex 1485 wcel 2141 wrex 2449 cop 3586 ciun 3873 class class class wbr 3989 ccom 4615 wrel 4616 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-iun 3875 df-br 3990 df-opab 4051 df-xp 4617 df-rel 4618 df-co 4620 |
This theorem is referenced by: (None) |
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