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Theorem trv 4306
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 3360 . 2  |-  U. _V  C_ 
_V
2 df-tr 4295 . 2  |-  ( Tr 
_V 
<-> 
U. _V  C_  _V )
31, 2mpbir 201 1  |-  Tr  _V
Colors of variables: wff set class
Syntax hints:   _Vcvv 2948    C_ wss 3312   U.cuni 4007   Tr wtr 4294
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-v 2950  df-in 3319  df-ss 3326  df-tr 4295
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