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Theorem dftr4 5266
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 5260 . 2 (Tr 𝐴 𝐴𝐴)
2 sspwuni 5100 . 2 (𝐴 ⊆ 𝒫 𝐴 𝐴𝐴)
31, 2bitr4i 278 1 (Tr 𝐴𝐴 ⊆ 𝒫 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 206  wss 3951  𝒫 cpw 4600   cuni 4907  Tr wtr 5259
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3062  df-v 3482  df-ss 3968  df-pw 4602  df-uni 4908  df-tr 5260
This theorem is referenced by:  tr0  5272  pwtr  5457  r1ordg  9818  r1sssuc  9823  r1val1  9826  ackbij2lem3  10280  tsktrss  10801
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