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Theorem dftr4 4892
Description: An alternate way of defining a transitive class. Definition of [Enderton] p. 71. (Contributed by NM, 29-Aug-1993.)
Assertion
Ref Expression
dftr4 (Tr 𝐴𝐴 ⊆ 𝒫 𝐴)

Proof of Theorem dftr4
StepHypRef Expression
1 df-tr 4888 . 2 (Tr 𝐴 𝐴𝐴)
2 sspwuni 4746 . 2 (𝐴 ⊆ 𝒫 𝐴 𝐴𝐴)
31, 2bitr4i 267 1 (Tr 𝐴𝐴 ⊆ 𝒫 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wss 3723  𝒫 cpw 4298   cuni 4575  Tr wtr 4887
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-ral 3066  df-v 3353  df-in 3730  df-ss 3737  df-pw 4300  df-uni 4576  df-tr 4888
This theorem is referenced by:  tr0  4898  pwtr  5050  r1ordg  8809  r1sssuc  8814  r1val1  8817  ackbij2lem3  9269  tsktrss  9789
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