Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > opeldm | Unicode version |
Description: Membership of first of an ordered pair in a domain. (Contributed by NM, 30-Jul-1995.) |
Ref | Expression |
---|---|
opeldm.1 | |
opeldm.2 |
Ref | Expression |
---|---|
opeldm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opeldm.2 | . . 3 | |
2 | opeq2 3764 | . . . 4 | |
3 | 2 | eleq1d 2239 | . . 3 |
4 | 1, 3 | spcev 2825 | . 2 |
5 | opeldm.1 | . . 3 | |
6 | 5 | eldm2 4807 | . 2 |
7 | 4, 6 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wex 1485 wcel 2141 cvv 2730 cop 3584 cdm 4609 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-sn 3587 df-pr 3588 df-op 3590 df-br 3988 df-dm 4619 |
This theorem is referenced by: breldm 4813 elreldm 4835 relssres 4927 iss 4935 imadmrn 4961 dfco2a 5109 funssres 5238 funun 5240 iinerm 6582 |
Copyright terms: Public domain | W3C validator |