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Theorem trv 5181
 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 3995 . 2 V ⊆ V
2 df-tr 5170 . 2 (Tr V ↔ V ⊆ V)
31, 2mpbir 232 1 Tr V
 Colors of variables: wff setvar class Syntax hints:  Vcvv 3500   ⊆ wss 3940  ∪ cuni 4837  Tr wtr 5169 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2805  df-cleq 2819  df-clel 2898  df-v 3502  df-in 3947  df-ss 3956  df-tr 5170 This theorem is referenced by: (None)
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