Theorem trv 5186

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 3993	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5175	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 233	1 ⊢ Tr V

Syntax hints:  Vcvv 3496   ⊆ wss 3938  ∪ cuni 4840  Tr wtr 5174

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 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2795

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2802  df-cleq 2816  df-clel 2895  df-v 3498  df-in 3945  df-ss 3954  df-tr 5175

This theorem is referenced by: (None)