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Theorem unv 3647
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 3360 . 2  |-  ( A  u.  _V )  C_  _V
2 ssun2 3503 . 2  |-  _V  C_  ( A  u.  _V )
31, 2eqssi 3356 1  |-  ( A  u.  _V )  =  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1652   _Vcvv 2948    u. cun 3310
This theorem is referenced by:  oev2  6758
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-in 3319  df-ss 3326
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