Theorem trv 5231

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 3960	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5218	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 234	1 ⊢ Tr V

This proof depends on syntax axioms:  Vcvv 3454   ⊆ wss 3904  ∪ cuni 4871  Tr wtr 5217

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-tru 1572  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3456  df-ss 3921  df-tr 5218

This theorem is used by: (None)