Theorem trv 5279

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 4020	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5266	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 231	1 ⊢ Tr V

Syntax hints:  Vcvv 3478   ⊆ wss 3963  ∪ cuni 4912  Tr wtr 5265

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-ss 3980  df-tr 5266

This theorem is referenced by: (None)