Theorem trv 4046

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 3124	. 2 |- U. _V C_ _V
2		df-tr 4035	. 2 |- ( Tr _V <-> U. _V C_ _V )
3	1, 2	mpbir 145	1 |- Tr _V

Syntax hints:   _Vcvv 2689   C_ wss 3076   U.cuni 3744   Tr wtr 4034

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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-v 2691  df-in 3082  df-ss 3089  df-tr 4035

This theorem is referenced by: (None)