Theorem trv 4033

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 3114	. 2 ⊢ ∪ V ⊆ V
2		df-tr 4022	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 145	1 ⊢ Tr V

Syntax hints:  Vcvv 2681   ⊆ wss 3066  ∪ cuni 3731  Tr wtr 4021

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-v 2683  df-in 3072  df-ss 3079  df-tr 4022

This theorem is referenced by: (None)