Theorem trv 5297

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 4033	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5284	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 231	1 ⊢ Tr V

Syntax hints:  Vcvv 3488   ⊆ wss 3976  ∪ cuni 4931  Tr wtr 5283

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-ss 3993  df-tr 5284

This theorem is referenced by: (None)