Theorem trv 4193

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 3246	. 2 ⊢ ∪ V ⊆ V
2		df-tr 4182	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 146	1 ⊢ Tr V

Syntax hints:  Vcvv 2799   ⊆ wss 3197  ∪ cuni 3887  Tr wtr 4181

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-v 2801  df-in 3203  df-ss 3210  df-tr 4182

This theorem is referenced by: (None)