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Theorem tr0 4124
Description: The empty set is transitive. (Contributed by NM, 16-Sep-1993.)
Assertion
Ref Expression
tr0  |-  Tr  (/)

Proof of Theorem tr0
StepHypRef Expression
1 0ss 3483 . 2  |-  (/)  C_  ~P (/)
2 dftr4 4118 . 2  |-  ( Tr  (/) 
<->  (/)  C_  ~P (/) )
31, 2mpbir 200 1  |-  Tr  (/)
Colors of variables: wff set class
Syntax hints:    C_ wss 3152   (/)c0 3455   ~Pcpw 3625   Tr wtr 4113
This theorem is referenced by:  ord0  4444  tctr  7425  tc0  7432  r1tr  7448
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-v 2790  df-dif 3155  df-in 3159  df-ss 3166  df-nul 3456  df-pw 3627  df-uni 3828  df-tr 4114
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