Theorem trv 2692

Description: The universe is transitive.

Assertion

Ref	Expression
trv	|- Tr V

Proof of Theorem trv

Step	Hyp	Ref	Expression
1		ssv 2081	. 2 |- U.V (_ V
2		df-tr 2681	. 2 |- (Tr V <-> U.V (_ V)
3	1, 2	mpbir 190	1 |- Tr V

Syntax hints:  Vcvv 1811   (_ wss 2047  U.cuni 2503  Tr wtr 2680

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-in 2051  df-ss 2053  df-tr 2681

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