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Theorem trv 4125
Description: The universe is transitive. (Contributed by NM, 14-Sep-2003.)
Assertion
Ref Expression
trv  |-  Tr  _V

Proof of Theorem trv
StepHypRef Expression
1 ssv 3198 . 2  |-  U. _V  C_ 
_V
2 df-tr 4114 . 2  |-  ( Tr 
_V 
<-> 
U. _V  C_  _V )
31, 2mpbir 200 1  |-  Tr  _V
Colors of variables: wff set class
Syntax hints:   _Vcvv 2788    C_ wss 3152   U.cuni 3827   Tr wtr 4113
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-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-v 2790  df-in 3159  df-ss 3166  df-tr 4114
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