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Theorem dftr5 4297
 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 4296 . 2
2 alcom 1752 . . 3
3 impexp 434 . . . . . . . 8
43albii 1575 . . . . . . 7
5 df-ral 2702 . . . . . . 7
64, 5bitr4i 244 . . . . . 6
7 r19.21v 2785 . . . . . 6
86, 7bitri 241 . . . . 5
98albii 1575 . . . 4
10 df-ral 2702 . . . 4
119, 10bitr4i 244 . . 3
122, 11bitri 241 . 2
131, 12bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wcel 1725  wral 2697   wtr 4294 This theorem is referenced by:  dftr3  4298  smobeth  8451 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-v 2950  df-in 3319  df-ss 3326  df-uni 4008  df-tr 4295
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