Theorem trv 4154

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 3215	. 2 |- U. _V C_ _V
2		df-tr 4143	. 2 |- ( Tr _V <-> U. _V C_ _V )
3	1, 2	mpbir 146	1 |- Tr _V

Syntax hints:   _Vcvv 2772   C_ wss 3166   U.cuni 3850   Tr wtr 4142

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-v 2774  df-in 3172  df-ss 3179  df-tr 4143

This theorem is referenced by: (None)