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Theorem trv 5240
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 3972 . 2 V ⊆ V
2 df-tr 5227 . 2 (Tr V ↔ V ⊆ V)
31, 2mpbir 230 1 Tr V
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3447  wss 3914   cuni 4869  Tr wtr 5226
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3449  df-in 3921  df-ss 3931  df-tr 5227
This theorem is referenced by: (None)
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