Theorem trv 3887

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 3019	. 2 ⊢ ∪ V ⊆ V
2		df-tr 3876	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 144	1 ⊢ Tr V

Syntax hints:  Vcvv 2601   ⊆ wss 2973  ∪ cuni 3601  Tr wtr 3875

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 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-v 2603  df-in 2979  df-ss 2986  df-tr 3876

This theorem is referenced by: (None)