Theorem trv 4693

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 3588	. 2 ⊢ ∪ V ⊆ V
2		df-tr 4681	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 220	1 ⊢ Tr V

Syntax hints:  Vcvv 3173   ⊆ wss 3540  ∪ cuni 4372  Tr wtr 4680

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-v 3175  df-in 3547  df-ss 3554  df-tr 4681

This theorem is referenced by: (None)