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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 4036 | . . 3 | |
2 | nfopab2 4037 | . . 3 | |
3 | 1, 2 | dfdmf 4782 | . 2 |
4 | df-br 3968 | . . . . 5 | |
5 | opabid 4220 | . . . . 5 | |
6 | 4, 5 | bitri 183 | . . . 4 |
7 | 6 | exbii 1585 | . . 3 |
8 | 7 | abbii 2273 | . 2 |
9 | 3, 8 | eqtri 2178 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1335 wex 1472 wcel 2128 cab 2143 cop 3564 class class class wbr 3967 copab 4027 cdm 4589 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4085 ax-pow 4138 ax-pr 4172 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-br 3968 df-opab 4029 df-dm 4599 |
This theorem is referenced by: dmopabss 4801 dmopab3 4802 fndmin 5577 dmoprab 5905 shftdm 10734 |
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