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Theorem trv 4141
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 3211 . 2  |-  U. _V  C_ 
_V
2 df-tr 4130 . 2  |-  ( Tr 
_V 
<-> 
U. _V  C_  _V )
31, 2mpbir 200 1  |-  Tr  _V
Colors of variables: wff set class
Syntax hints:   _Vcvv 2801    C_ wss 3165   U.cuni 3843   Tr wtr 4129
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-v 2803  df-in 3172  df-ss 3179  df-tr 4130
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