Theorem unv 3452

Description: The union of a class with the universal class is the universal class. Exercise 4.10(l) of [Mendelson] p. 231. (Contributed by NM, 17-May-1998.)

Assertion

Ref	Expression
unv	|- ( A u. _V ) = _V

Proof of Theorem unv

Step	Hyp	Ref	Expression
1		ssv 3169	. 2 |- ( A u. _V ) C_ _V
2		ssun2 3291	. 2 |- _V C_ ( A u. _V )
3	1, 2	eqssi 3163	1 |- ( A u. _V ) = _V

Syntax hints:   = wceq 1348   _Vcvv 2730   u. cun 3119

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-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125  df-in 3127  df-ss 3134

This theorem is referenced by: (None)