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Theorem unv 3787
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 3481 . 2  |-  ( A  u.  _V )  C_  _V
2 ssun2 3627 . 2  |-  _V  C_  ( A  u.  _V )
31, 2eqssi 3477 1  |-  ( A  u.  _V )  =  _V
Colors of variables: wff setvar class
Syntax hints:    = wceq 1437   _Vcvv 3078    u. cun 3431
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-v 3080  df-un 3438  df-in 3440  df-ss 3447
This theorem is referenced by:  oev2  7225
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