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Theorem unv 3578
 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 ∪ V) = V

Proof of Theorem unv
StepHypRef Expression
1 ssv 3291 . 2 (A ∪ V) V
2 ssun2 3427 . 2 V (A ∪ V)
31, 2eqssi 3288 1 (A ∪ V) = V
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642  Vcvv 2859   ∪ cun 3207 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-ss 3259 This theorem is referenced by: (None)
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