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Theorem trv 4143
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 3205 . 2 V ⊆ V
2 df-tr 4132 . 2 (Tr V ↔ V ⊆ V)
31, 2mpbir 146 1 Tr V
Colors of variables: wff set class
Syntax hints:  Vcvv 2763  wss 3157   cuni 3839  Tr wtr 4131
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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-11 1520  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178
This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-v 2765  df-in 3163  df-ss 3170  df-tr 4132
This theorem is referenced by: (None)
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