Theorem trv 5273

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 4008	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5260	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 231	1 ⊢ Tr V

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)