Theorem trv 3424

Description: The universe is transitive.

Assertion

Ref	Expression
trv	|- Tr _V

Proof of Theorem trv

Step	Hyp	Ref	Expression
1		ssv 2636	. 2 |- U._V C_ _V
2		df-tr 3412	. 2 |- (Tr _V <-> U._V C_ _V)
3	1, 2	mpbir 207	1 |- Tr _V

Syntax hints:  _Vcvv 2292   C_ wss 2593  U.cuni 3177  Tr wtr 3411

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-10 1308  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-v 2294  df-in 2603  df-ss 2605  df-tr 3412

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