MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  unv Unicode version

Theorem unv 3483
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
StepHypRef Expression
1 ssv 3199 . 2  |-  ( A  u.  _V )  C_  _V
2 ssun2 3340 . 2  |-  _V  C_  ( A  u.  _V )
31, 2eqssi 3196 1  |-  ( A  u.  _V )  =  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1624   _Vcvv 2789    u. cun 3151
This theorem is referenced by:  oev2  6517
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1867  ax-ext 2265
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1312  df-ex 1530  df-nf 1533  df-sb 1632  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-v 2791  df-un 3158  df-in 3160  df-ss 3167
  Copyright terms: Public domain W3C validator