Theorem trv 4099

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 3169	. 2 |- U. _V C_ _V
2		df-tr 4088	. 2 |- ( Tr _V <-> U. _V C_ _V )
3	1, 2	mpbir 145	1 |- Tr _V

Syntax hints:   _Vcvv 2730   C_ wss 3121   U.cuni 3796   Tr wtr 4087

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 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-v 2732  df-in 3127  df-ss 3134  df-tr 4088

This theorem is referenced by: (None)