Theorem trv 5223

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 3962	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5210	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 233	1 ⊢ Tr V

Syntax hints:  Vcvv 3456   ⊆ wss 3906  ∪ cuni 4867  Tr wtr 5209

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989  ax-7 2030  ax-8 2146  ax-9 2154  ax-ext 2736

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1565  df-ex 1802  df-sb 2093  df-clab 2743  df-cleq 2756  df-clel 2839  df-v 3458  df-ss 3923  df-tr 5210

This theorem is referenced by: (None)