Theorem unv 3484

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 3201	. 2 |- ( A u. _V ) C_ _V
2		ssun2 3323	. 2 |- _V C_ ( A u. _V )
3	1, 2	eqssi 3195	1 |- ( A u. _V ) = _V

Syntax hints:   = wceq 1364   _Vcvv 2760   u. cun 3151

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-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3157  df-in 3159  df-ss 3166

This theorem is referenced by: (None)