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Mirrors > Home > ILE Home > Th. List > dmopab3 | Unicode version |
Description: The domain of a restricted class of ordered pairs. (Contributed by NM, 31-Jan-2004.) |
Ref | Expression |
---|---|
dmopab3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2311 | . 2 | |
2 | pm4.71 369 | . . 3 | |
3 | 2 | albii 1359 | . 2 |
4 | dmopab 4546 | . . . . 5 | |
5 | 19.42v 1786 | . . . . . 6 | |
6 | 5 | abbii 2153 | . . . . 5 |
7 | 4, 6 | eqtri 2060 | . . . 4 |
8 | 7 | eqeq1i 2047 | . . 3 |
9 | eqcom 2042 | . . 3 | |
10 | abeq2 2146 | . . 3 | |
11 | 8, 9, 10 | 3bitr2ri 198 | . 2 |
12 | 1, 3, 11 | 3bitri 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wex 1381 wcel 1393 cab 2026 wral 2306 copab 3817 cdm 4345 |
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-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-dm 4355 |
This theorem is referenced by: dmxpm 4555 fnopabg 5022 |
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