Theorem trv 5176

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 3990	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5165	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 233	1 ⊢ Tr V

Syntax hints:  Vcvv 3494   ⊆ wss 3935  ∪ cuni 4831  Tr wtr 5164

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2157  ax-12 2173  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1536  df-ex 1777  df-nf 1781  df-sb 2066  df-clab 2800  df-cleq 2814  df-clel 2893  df-v 3496  df-in 3942  df-ss 3951  df-tr 5165

This theorem is referenced by: (None)