Theorem trv 5280

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 4007	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5267	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 230	1 ⊢ Tr V

Syntax hints:  Vcvv 3475   ⊆ wss 3949  ∪ cuni 4909  Tr wtr 5266

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 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3956  df-ss 3966  df-tr 5267

This theorem is referenced by: (None)