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Theorem dftr4 4685
 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 4681 . 2 (Tr 𝐴 𝐴𝐴)
2 sspwuni 4547 . 2 (𝐴 ⊆ 𝒫 𝐴 𝐴𝐴)
31, 2bitr4i 266 1 (Tr 𝐴𝐴 ⊆ 𝒫 𝐴)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 195   ⊆ wss 3540  𝒫 cpw 4108  ∪ cuni 4372  Tr wtr 4680 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-v 3175  df-in 3547  df-ss 3554  df-pw 4110  df-uni 4373  df-tr 4681 This theorem is referenced by:  tr0  4692  pwtr  4848  r1ordg  8524  r1sssuc  8529  r1val1  8532  ackbij2lem3  8946  tsktrss  9462
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