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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 4764 | . . . 4 | |
2 | eluni2 3776 | . . . . . . 7 | |
3 | 2 | anbi2i 453 | . . . . . 6 |
4 | r19.42v 2614 | . . . . . 6 | |
5 | 3, 4 | bitr4i 186 | . . . . 5 |
6 | 5 | 2exbii 1586 | . . . 4 |
7 | elcnv2 4764 | . . . . . 6 | |
8 | 7 | rexbii 2464 | . . . . 5 |
9 | rexcom4 2735 | . . . . 5 | |
10 | rexcom4 2735 | . . . . . 6 | |
11 | 10 | exbii 1585 | . . . . 5 |
12 | 8, 9, 11 | 3bitrri 206 | . . . 4 |
13 | 1, 6, 12 | 3bitri 205 | . . 3 |
14 | eliun 3853 | . . 3 | |
15 | 13, 14 | bitr4i 186 | . 2 |
16 | 15 | eqriv 2154 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1335 wex 1472 wcel 2128 wrex 2436 cop 3563 cuni 3772 ciun 3849 ccnv 4585 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-iun 3851 df-br 3966 df-opab 4026 df-cnv 4594 |
This theorem is referenced by: funcnvuni 5239 |
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