ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  dftr4 GIF version

Theorem dftr4 4037
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 4033 . 2 (Tr 𝐴 𝐴𝐴)
2 sspwuni 3903 . 2 (𝐴 ⊆ 𝒫 𝐴 𝐴𝐴)
31, 2bitr4i 186 1 (Tr 𝐴𝐴 ⊆ 𝒫 𝐴)
Colors of variables: wff set class
Syntax hints:  wb 104  wss 3074  𝒫 cpw 3513   cuni 3742  Tr wtr 4032
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-v 2691  df-in 3080  df-ss 3087  df-pw 3515  df-uni 3743  df-tr 4033
This theorem is referenced by:  tr0  4043  pwtr  4147
  Copyright terms: Public domain W3C validator