Theorem trv 4111

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 3177	. 2 ⊢ ∪ V ⊆ V
2		df-tr 4100	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 146	1 ⊢ Tr V

Syntax hints:  Vcvv 2737   ⊆ wss 3129  ∪ cuni 3808  Tr wtr 4099

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-v 2739  df-in 3135  df-ss 3142  df-tr 4100

This theorem is referenced by: (None)