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Theorem unv 3495
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 3211 . 2  |-  ( A  u.  _V )  C_  _V
2 ssun2 3352 . 2  |-  _V  C_  ( A  u.  _V )
31, 2eqssi 3208 1  |-  ( A  u.  _V )  =  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1632   _Vcvv 2801    u. cun 3163
This theorem is referenced by:  oev2  6538
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-in 3172  df-ss 3179
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