Theorem trv 4765

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 3625	. 2 |- U. _V C_ _V
2		df-tr 4753	. 2 |- ( Tr _V <-> U. _V C_ _V )
3	1, 2	mpbir 221	1 |- Tr _V

Syntax hints:   _Vcvv 3200   C_ wss 3574   U.cuni 4436   Tr wtr 4752

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-v 3202  df-in 3581  df-ss 3588  df-tr 4753

This theorem is referenced by: (None)