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Theorem trv 3857
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 2959 . 2 V ⊆ V
2 df-tr 3846 . 2 (Tr V ↔ V ⊆ V)
31, 2mpbir 134 1 Tr V
Colors of variables: wff set class
Syntax hints:  Vcvv 2551  wss 2911   cuni 3571  Tr wtr 3845
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553  df-in 2918  df-ss 2925  df-tr 3846
This theorem is referenced by: (None)
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