Theorem trv 4222

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 3262	. 2 |- U. _V C_ _V
2		df-tr 4211	. 2 |- ( Tr _V <-> U. _V C_ _V )
3	1, 2	mpbir 146	1 |- Tr _V

Syntax hints:   _Vcvv 2815   C_ wss 3213   U.cuni 3916   Tr wtr 4210

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-v 2817  df-in 3219  df-ss 3226  df-tr 4211

This theorem is referenced by: (None)