Theorem trv 5199

Description: The universe is transitive. (Contributed by NM, 14-Sep-2003.)

Assertion

Ref	Expression
trv	⊢ Tr V

Proof of Theorem trv

Step	Hyp	Ref	Expression
1		ssv 3941	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5188	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 230	1 ⊢ Tr V

Syntax hints:  Vcvv 3422   ⊆ wss 3883  ∪ cuni 4836  Tr wtr 5187

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-in 3890  df-ss 3900  df-tr 5188

This theorem is referenced by: (None)