Theorem trv 4239

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 3270	. 2 ⊢ ∪ V ⊆ V
2		df-tr 4228	. 2 ⊢ (Tr V ↔ ∪ V ⊆ V)
3	1, 2	mpbir 146	1 ⊢ Tr V

Syntax hints:  Vcvv 2821   ⊆ wss 3220  ∪ cuni 3933  Tr wtr 4227

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 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-v 2823  df-in 3226  df-ss 3233  df-tr 4228

This theorem is referenced by: (None)