Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > uniopel | Unicode version |
Description: Ordered pair membership is inherited by class union. (Contributed by NM, 13-May-2008.) (Revised by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
opthw.1 | |
opthw.2 |
Ref | Expression |
---|---|
uniopel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opthw.1 | . . . 4 | |
2 | opthw.2 | . . . 4 | |
3 | 1, 2 | uniop 3992 | . . 3 |
4 | 1, 2 | opi2 3970 | . . 3 |
5 | 3, 4 | eqeltri 2110 | . 2 |
6 | elssuni 3608 | . . 3 | |
7 | 6 | sseld 2944 | . 2 |
8 | 5, 7 | mpi 15 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1393 cvv 2557 cpr 3376 cop 3378 cuni 3580 |
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-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 |
This theorem is referenced by: dmrnssfld 4595 unielrel 4845 |
Copyright terms: Public domain | W3C validator |