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 4010 | . . 3 |
4 | 1, 2 | opi2 3988 | . . 3 |
5 | 3, 4 | eqeltri 2151 | . 2 |
6 | elssuni 3629 | . . 3 | |
7 | 6 | sseld 2998 | . 2 |
8 | 5, 7 | mpi 15 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1433 cvv 2601 cpr 3399 cop 3401 cuni 3601 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 |
This theorem is referenced by: dmrnssfld 4613 unielrel 4865 |
Copyright terms: Public domain | W3C validator |