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Theorem unv 3424
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 3140 . 2  |-  ( A  u.  _V )  C_  _V
2 ssun2 3281 . 2  |-  _V  C_  ( A  u.  _V )
31, 2eqssi 3137 1  |-  ( A  u.  _V )  =  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1619   _Vcvv 2740    u. cun 3092
This theorem is referenced by:  oev2  6455
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-v 2742  df-un 3099  df-in 3101  df-ss 3108
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