Theorem trv 5225

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 3932	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5212	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 234	1 ⊢ Tr V

This proof depends on syntax axioms:  Vcvv 3450   ⊆ wss 3895  ∪ cuni 4866  Tr wtr 5211

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-tr 5212

This theorem is used by: (None)