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Theorem dftr5 4265
 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 4264 . 2
2 alcom 1748 . . 3
3 impexp 434 . . . . . . . 8
43albii 1572 . . . . . . 7
5 df-ral 2671 . . . . . . 7
64, 5bitr4i 244 . . . . . 6
7 r19.21v 2753 . . . . . 6
86, 7bitri 241 . . . . 5
98albii 1572 . . . 4
10 df-ral 2671 . . . 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 1546   wcel 1721  wral 2666   wtr 4262 This theorem is referenced by:  dftr3  4266  smobeth  8417 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ral 2671  df-v 2918  df-in 3287  df-ss 3294  df-uni 3976  df-tr 4263
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