Theorem trv 5195

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 3940	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5182	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 233	1 ⊢ Tr V

Syntax hints:  Vcvv 3433   ⊆ wss 3884  ∪ cuni 4840  Tr wtr 5181

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1975  ax-7 2016  ax-8 2123  ax-9 2131  ax-ext 2713

This theorem depends on definitions:  df-bi 209  df-an 398  df-tru 1551  df-ex 1788  df-sb 2075  df-clab 2720  df-cleq 2733  df-clel 2816  df-v 3435  df-ss 3901  df-tr 5182

This theorem is referenced by: (None)