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Theorem dftr2 3819
Description: An alternate way of defining a transitive class. Exercise 7 of [TakeutiZaring] p. 40. (Contributed by NM, 24-Apr-1994.)
Assertion
Ref Expression
dftr2  Tr
Distinct variable group:   ,,

Proof of Theorem dftr2
StepHypRef Expression
1 dfss2 2902 . 2  U.  C_  U.
2 df-tr 3818 . 2  Tr  U.  C_
3 19.23v 1736 . . . 4
4 eluni 3546 . . . . 5  U.
54imbi1i 227 . . . 4  U.
63, 5bitr4i 176 . . 3  U.
76albii 1332 . 2 
U.
81, 2, 73bitr4i 201 1  Tr
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1221  wex 1354   wcel 1366    C_ wss 2885   U.cuni 3543   Tr wtr 3817
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 614  ax-5 1309  ax-7 1310  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-8 1368  ax-10 1369  ax-11 1370  ax-i12 1371  ax-bnd 1372  ax-4 1373  ax-17 1392  ax-i9 1396  ax-ial 1400  ax-i5r 1401  ax-ext 1995
This theorem depends on definitions:  df-bi 110  df-tru 1226  df-nf 1323  df-sb 1619  df-clab 2000  df-cleq 2006  df-clel 2009  df-nfc 2140  df-v 2528  df-in 2892  df-ss 2899  df-uni 3544  df-tr 3818
This theorem is referenced by:  dftr5  3820  trel  3824  suctr  4096  ordtriexmidlem  4180  onsucelsucexmidlem  4186  ordsuc  4213  tfi  4220  ordom  4244
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