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Theorem unv 4004
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 3658 . 2 (𝐴 ∪ V) ⊆ V
2 ssun2 3810 . 2 V ⊆ (𝐴 ∪ V)
31, 2eqssi 3652 1 (𝐴 ∪ V) = V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1523  Vcvv 3231  cun 3605
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-un 3612  df-in 3614  df-ss 3621
This theorem is referenced by:  oev2  7648
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