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Theorem trv 3894
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 2993 . 2  |-  U. _V  C_ 
_V
2 df-tr 3883 . 2  |-  ( Tr 
_V 
<-> 
U. _V  C_  _V )
31, 2mpbir 138 1  |-  Tr  _V
Colors of variables: wff set class
Syntax hints:   _Vcvv 2574    C_ wss 2945   U.cuni 3608   Tr wtr 3882
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-v 2576  df-in 2952  df-ss 2959  df-tr 3883
This theorem is referenced by: (None)
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