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Theorem dftr4 5262
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 5256 . 2 (Tr 𝐴 𝐴𝐴)
2 sspwuni 5093 . 2 (𝐴 ⊆ 𝒫 𝐴 𝐴𝐴)
31, 2bitr4i 278 1 (Tr 𝐴𝐴 ⊆ 𝒫 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 205  wss 3940  𝒫 cpw 4594   cuni 4899  Tr wtr 5255
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-ral 3054  df-v 3468  df-in 3947  df-ss 3957  df-pw 4596  df-uni 4900  df-tr 5256
This theorem is referenced by:  tr0  5268  pwtr  5442  r1ordg  9769  r1sssuc  9774  r1val1  9777  ackbij2lem3  10232  tsktrss  10752
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