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Theorem trv 4923
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 3785 . 2 V ⊆ V
2 df-tr 4912 . 2 (Tr V ↔ V ⊆ V)
31, 2mpbir 222 1 Tr V
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3350  wss 3732   cuni 4594  Tr wtr 4911
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2069  ax-7 2105  ax-9 2164  ax-10 2183  ax-11 2198  ax-12 2211  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 874  df-tru 1656  df-ex 1875  df-nf 1879  df-sb 2062  df-clab 2752  df-cleq 2758  df-clel 2761  df-v 3352  df-in 3739  df-ss 3746  df-tr 4912
This theorem is referenced by: (None)
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