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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 4789 | . . . 4 | |
2 | eluni2 3800 | . . . . . . 7 | |
3 | 2 | anbi2i 454 | . . . . . 6 |
4 | r19.42v 2627 | . . . . . 6 | |
5 | 3, 4 | bitr4i 186 | . . . . 5 |
6 | 5 | 2exbii 1599 | . . . 4 |
7 | elcnv2 4789 | . . . . . 6 | |
8 | 7 | rexbii 2477 | . . . . 5 |
9 | rexcom4 2753 | . . . . 5 | |
10 | rexcom4 2753 | . . . . . 6 | |
11 | 10 | exbii 1598 | . . . . 5 |
12 | 8, 9, 11 | 3bitrri 206 | . . . 4 |
13 | 1, 6, 12 | 3bitri 205 | . . 3 |
14 | eliun 3877 | . . 3 | |
15 | 13, 14 | bitr4i 186 | . 2 |
16 | 15 | eqriv 2167 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 wex 1485 wcel 2141 wrex 2449 cop 3586 cuni 3796 ciun 3873 ccnv 4610 |
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-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-uni 3797 df-iun 3875 df-br 3990 df-opab 4051 df-cnv 4619 |
This theorem is referenced by: funcnvuni 5267 |
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