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Mirrors > Home > ILE Home > Th. List > cnvuni | Unicode version |
Description: The converse of a class union is the (indexed) union of the converses of its members. (Contributed by NM, 11-Aug-2004.) |
Ref | Expression |
---|---|
cnvuni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elcnv2 4712 | . . . 4 | |
2 | eluni2 3735 | . . . . . . 7 | |
3 | 2 | anbi2i 452 | . . . . . 6 |
4 | r19.42v 2586 | . . . . . 6 | |
5 | 3, 4 | bitr4i 186 | . . . . 5 |
6 | 5 | 2exbii 1585 | . . . 4 |
7 | elcnv2 4712 | . . . . . 6 | |
8 | 7 | rexbii 2440 | . . . . 5 |
9 | rexcom4 2704 | . . . . 5 | |
10 | rexcom4 2704 | . . . . . 6 | |
11 | 10 | exbii 1584 | . . . . 5 |
12 | 8, 9, 11 | 3bitrri 206 | . . . 4 |
13 | 1, 6, 12 | 3bitri 205 | . . 3 |
14 | eliun 3812 | . . 3 | |
15 | 13, 14 | bitr4i 186 | . 2 |
16 | 15 | eqriv 2134 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 wex 1468 wcel 1480 wrex 2415 cop 3525 cuni 3731 ciun 3808 ccnv 4533 |
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-ral 2419 df-rex 2420 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-uni 3732 df-iun 3810 df-br 3925 df-opab 3985 df-cnv 4542 |
This theorem is referenced by: funcnvuni 5187 |
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