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Theorem dftr4 4679
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 4675 . 2 (Tr 𝐴 𝐴𝐴)
2 sspwuni 4541 . 2 (𝐴 ⊆ 𝒫 𝐴 𝐴𝐴)
31, 2bitr4i 265 1 (Tr 𝐴𝐴 ⊆ 𝒫 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 194  wss 3539  𝒫 cpw 4107   cuni 4366  Tr wtr 4674
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-ral 2900  df-v 3174  df-in 3546  df-ss 3553  df-pw 4109  df-uni 4367  df-tr 4675
This theorem is referenced by:  tr0  4686  pwtr  4842  r1ordg  8501  r1sssuc  8506  r1val1  8509  ackbij2lem3  8923  tsktrss  9439
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