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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 3086 | . 2 | |
2 | df-tr 4027 | . 2 | |
3 | 19.23v 1855 | . . . 4 | |
4 | eluni 3739 | . . . . 5 | |
5 | 4 | imbi1i 237 | . . . 4 |
6 | 3, 5 | bitr4i 186 | . . 3 |
7 | 6 | albii 1446 | . 2 |
8 | 1, 2, 7 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wex 1468 wcel 1480 wss 3071 cuni 3736 wtr 4026 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-in 3077 df-ss 3084 df-uni 3737 df-tr 4027 |
This theorem is referenced by: dftr5 4029 trel 4033 suctr 4343 ordtriexmidlem 4435 ordtri2or2exmidlem 4441 onsucelsucexmidlem 4444 ordsuc 4478 tfi 4496 ordom 4520 |
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