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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 4513 | . . . 4 | |
2 | eluni2 3584 | . . . . . . 7 | |
3 | 2 | anbi2i 430 | . . . . . 6 |
4 | r19.42v 2467 | . . . . . 6 | |
5 | 3, 4 | bitr4i 176 | . . . . 5 |
6 | 5 | 2exbii 1497 | . . . 4 |
7 | elcnv2 4513 | . . . . . 6 | |
8 | 7 | rexbii 2331 | . . . . 5 |
9 | rexcom4 2577 | . . . . 5 | |
10 | rexcom4 2577 | . . . . . 6 | |
11 | 10 | exbii 1496 | . . . . 5 |
12 | 8, 9, 11 | 3bitrri 196 | . . . 4 |
13 | 1, 6, 12 | 3bitri 195 | . . 3 |
14 | eliun 3661 | . . 3 | |
15 | 13, 14 | bitr4i 176 | . 2 |
16 | 15 | eqriv 2037 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wceq 1243 wex 1381 wcel 1393 wrex 2307 cop 3378 cuni 3580 ciun 3657 ccnv 4344 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-iun 3659 df-br 3765 df-opab 3819 df-cnv 4353 |
This theorem is referenced by: funcnvuni 4968 |
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