Theorem trv 5248

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 3988	. 2 ⊢ ∪ V ⊆ V
2		df-tr 5235	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 231	1 ⊢ Tr V

Syntax hints:  Vcvv 3464   ⊆ wss 3931  ∪ cuni 4888  Tr wtr 5234

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2715  df-cleq 2728  df-clel 2810  df-v 3466  df-ss 3948  df-tr 5235

This theorem is referenced by: (None)