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Theorem trv 4108
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 3175 . 2 V ⊆ V
2 df-tr 4097 . 2 (Tr V ↔ V ⊆ V)
31, 2mpbir 146 1 Tr V
Colors of variables: wff set class
Syntax hints:  Vcvv 2735  wss 3127   cuni 3805  Tr wtr 4096
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1445  ax-7 1446  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-8 1502  ax-11 1504  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532  ax-i5r 1533  ax-ext 2157
This theorem depends on definitions:  df-bi 117  df-nf 1459  df-sb 1761  df-clab 2162  df-cleq 2168  df-clel 2171  df-v 2737  df-in 3133  df-ss 3140  df-tr 4097
This theorem is referenced by: (None)
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