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Mirrors > Home > ILE Home > Th. List > dftr2 | Unicode version |
Description: An alternate way of defining a transitive class. Exercise 7 of [TakeutiZaring] p. 40. (Contributed by NM, 24-Apr-1994.) |
Ref | Expression |
---|---|
dftr2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfss2 2934 | . 2 | |
2 | df-tr 3855 | . 2 | |
3 | 19.23v 1763 | . . . 4 | |
4 | eluni 3583 | . . . . 5 | |
5 | 4 | imbi1i 227 | . . . 4 |
6 | 3, 5 | bitr4i 176 | . . 3 |
7 | 6 | albii 1359 | . 2 |
8 | 1, 2, 7 | 3bitr4i 201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wex 1381 wcel 1393 wss 2917 cuni 3580 wtr 3854 |
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-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 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-in 2924 df-ss 2931 df-uni 3581 df-tr 3855 |
This theorem is referenced by: dftr5 3857 trel 3861 suctr 4158 ordtriexmidlem 4245 ordtri2or2exmidlem 4251 onsucelsucexmidlem 4254 ordsuc 4287 tfi 4305 ordom 4329 |
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