Theorem trv 5216

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 3956	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5204	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 231	1 ⊢ Tr V

Syntax hints:  Vcvv 3438   ⊆ wss 3899  ∪ cuni 4861  Tr wtr 5203

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2713  df-cleq 2726  df-clel 2809  df-v 3440  df-ss 3916  df-tr 5204

This theorem is referenced by: (None)