Theorem trv 2682

Description: The universe is transitive.

Assertion

Ref	Expression
trv	|- Tr V

Proof of Theorem trv

Step	Hyp	Ref	Expression
1		ssv 2071	. 2 |- U.V (_ V
2		df-tr 2671	. 2 |- (Tr V <-> U.V (_ V)
3	1, 2	mpbir 190	1 |- Tr V

Syntax hints:  Vcvv 1802   (_ wss 2037  U.cuni 2493  Tr wtr 2670

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-v 1803  df-in 2041  df-ss 2043  df-tr 2671

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