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Theorem dftr4 5068
 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 5064 . 2 (Tr 𝐴 𝐴𝐴)
2 sspwuni 4921 . 2 (𝐴 ⊆ 𝒫 𝐴 𝐴𝐴)
31, 2bitr4i 279 1 (Tr 𝐴𝐴 ⊆ 𝒫 𝐴)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 207   ⊆ wss 3859  𝒫 cpw 4453  ∪ cuni 4745  Tr wtr 5063 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-8 2083  ax-9 2091  ax-10 2112  ax-11 2126  ax-12 2141  ax-ext 2769 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-tru 1525  df-ex 1762  df-nf 1766  df-sb 2043  df-clab 2776  df-cleq 2788  df-clel 2863  df-nfc 2935  df-ral 3110  df-v 3439  df-in 3866  df-ss 3874  df-pw 4455  df-uni 4746  df-tr 5064 This theorem is referenced by:  tr0  5074  pwtr  5237  r1ordg  9053  r1sssuc  9058  r1val1  9061  ackbij2lem3  9509  tsktrss  10029
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