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Theorem trv 4097
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 3169 . 2  |-  U. _V  C_ 
_V
2 df-tr 4086 . 2  |-  ( Tr 
_V 
<-> 
U. _V  C_  _V )
31, 2mpbir 145 1  |-  Tr  _V
Colors of variables: wff set class
Syntax hints:   _Vcvv 2730    C_ wss 3121   U.cuni 3794   Tr wtr 4085
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-v 2732  df-in 3127  df-ss 3134  df-tr 4086
This theorem is referenced by: (None)
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