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Theorem trv 5273
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 4008 . 2 V ⊆ V
2 df-tr 5260 . 2 (Tr V ↔ V ⊆ V)
31, 2mpbir 231 1 Tr V
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3480  wss 3951   cuni 4907  Tr wtr 5259
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-ss 3968  df-tr 5260
This theorem is referenced by: (None)
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