Theorem trv 5229

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 3937	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5216	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 234	1 ⊢ Tr V

This proof depends on syntax axioms:  Vcvv 3454   ⊆ wss 3900  ∪ cuni 4870  Tr wtr 5215

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-tr 5216

This theorem is used by: (None)