Theorem trv 5203

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 3945	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5192	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 230	1 ⊢ Tr V

Syntax hints:  Vcvv 3432   ⊆ wss 3887  ∪ cuni 4839  Tr wtr 5191

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-in 3894  df-ss 3904  df-tr 5192

This theorem is referenced by: (None)