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Theorem dftr5 4013
 Description: An alternate way of defining a transitive class. (Contributed by NM, 20-Mar-2004.)
Assertion
Ref Expression
dftr5
Distinct variable group:   ,,

Proof of Theorem dftr5
StepHypRef Expression
1 dftr2 4012 . 2
2 alcom 1568 . . 3
3 impexp 435 . . . . . . . 8
43albii 1554 . . . . . . 7
5 df-ral 2513 . . . . . . 7
64, 5bitr4i 245 . . . . . 6
7 r19.21v 2592 . . . . . 6
86, 7bitri 242 . . . . 5
98albii 1554 . . . 4
10 df-ral 2513 . . . 4
119, 10bitr4i 245 . . 3
122, 11bitri 242 . 2
131, 12bitri 242 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532   wcel 1621  wral 2509   wtr 4010 This theorem is referenced by:  dftr3  4014  smobeth  8088 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-v 2729  df-in 3085  df-ss 3089  df-uni 3728  df-tr 4011
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