Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > dmopab | Unicode version |
Description: The domain of a class of ordered pairs. (Contributed by NM, 16-May-1995.) (Revised by Mario Carneiro, 4-Dec-2016.) |
Ref | Expression |
---|---|
dmopab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfopab1 3997 | . . 3 | |
2 | nfopab2 3998 | . . 3 | |
3 | 1, 2 | dfdmf 4732 | . 2 |
4 | df-br 3930 | . . . . 5 | |
5 | opabid 4179 | . . . . 5 | |
6 | 4, 5 | bitri 183 | . . . 4 |
7 | 6 | exbii 1584 | . . 3 |
8 | 7 | abbii 2255 | . 2 |
9 | 3, 8 | eqtri 2160 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 wex 1468 wcel 1480 cab 2125 cop 3530 class class class wbr 3929 copab 3988 cdm 4539 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-dm 4549 |
This theorem is referenced by: dmopabss 4751 dmopab3 4752 fndmin 5527 dmoprab 5852 shftdm 10594 |
Copyright terms: Public domain | W3C validator |