Theorem unv 3326

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 3049	. 2 |- ( A u. _V ) C_ _V
2		ssun2 3167	. 2 |- _V C_ ( A u. _V )
3	1, 2	eqssi 3044	1 |- ( A u. _V ) = _V

Syntax hints:   = wceq 1290   _Vcvv 2622   u. cun 3000

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071

This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2624  df-un 3006  df-in 3008  df-ss 3015

This theorem is referenced by: (None)