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Theorem dftr5 4548
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 4547 . 2
2 alcom 1845 . . 3
3 impexp 446 . . . . . . . 8
43albii 1640 . . . . . . 7
5 df-ral 2812 . . . . . . 7
64, 5bitr4i 252 . . . . . 6
7 r19.21v 2862 . . . . . 6
86, 7bitri 249 . . . . 5
98albii 1640 . . . 4
10 df-ral 2812 . . . 4
119, 10bitr4i 252 . . 3
122, 11bitri 249 . 2
131, 12bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  e.wcel 1818  A.wral 2807  Trwtr 4545
This theorem is referenced by:  dftr3  4549  smobeth  8982
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-in 3482  df-ss 3489  df-uni 4250  df-tr 4546
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