Theorem trv 3866

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 2965	. 2 ⊢ ∪ V ⊆ V
2		df-tr 3855	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 134	1 ⊢ Tr V

Syntax hints:  Vcvv 2557   ⊆ wss 2917  ∪ cuni 3580  Tr wtr 3854

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559  df-in 2924  df-ss 2931  df-tr 3855

This theorem is referenced by: (None)