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Mirrors > Home > ILE Home > Th. List > opi2 | Unicode version |
Description: One of the two elements of an ordered pair. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
opi1.1 | |
opi1.2 |
Ref | Expression |
---|---|
opi2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opi1.1 | . . . 4 | |
2 | opi1.2 | . . . 4 | |
3 | prexgOLD 3946 | . . . 4 | |
4 | 1, 2, 3 | mp2an 402 | . . 3 |
5 | 4 | prid2 3477 | . 2 |
6 | 1, 2 | dfop 3548 | . 2 |
7 | 5, 6 | eleqtrri 2113 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1393 cvv 2557 csn 3375 cpr 3376 cop 3378 |
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-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-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-op 3384 |
This theorem is referenced by: uniopel 3993 opeluu 4182 elvvuni 4404 |
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