Theorem trv 3895

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 3020	. 2 ⊢ ∪ V ⊆ V
2		df-tr 3884	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 144	1 ⊢ Tr V

Syntax hints:  Vcvv 2602   ⊆ wss 2974  ∪ cuni 3609  Tr wtr 3883

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064

This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-v 2604  df-in 2980  df-ss 2987  df-tr 3884

This theorem is referenced by: (None)