Theorem trv 4038

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 3119	. 2 ⊢ ∪ V ⊆ V
2		df-tr 4027	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 145	1 ⊢ Tr V

Syntax hints:  Vcvv 2686   ⊆ wss 3071  ∪ cuni 3736  Tr wtr 4026

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 2121

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-v 2688  df-in 3077  df-ss 3084  df-tr 4027

This theorem is referenced by: (None)