Theorem trv 4070

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 3146	. 2 ⊢ ∪ V ⊆ V
2		df-tr 4059	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 145	1 ⊢ Tr V

Syntax hints:  Vcvv 2709   ⊆ wss 3098  ∪ cuni 3768  Tr wtr 4058

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-11 1483  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-v 2711  df-in 3104  df-ss 3111  df-tr 4059

This theorem is referenced by: (None)