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Theorem unv 4332
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 3977 . 2 (𝐴 ∪ V) ⊆ V
2 ssun2 4135 . 2 V ⊆ (𝐴 ∪ V)
31, 2eqssi 3969 1 (𝐴 ∪ V) = V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  Vcvv 3480  cun 3917
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482  df-un 3924  df-in 3926  df-ss 3936
This theorem is referenced by:  oev2  8144
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