Theorem trv 5148

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 3939	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5137	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 234	1 ⊢ Tr V

Syntax hints:  Vcvv 3441   ⊆ wss 3881  ∪ cuni 4800  Tr wtr 5136

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-in 3888  df-ss 3898  df-tr 5137

This theorem is referenced by: (None)