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Theorem unv 4356
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 3969 . 2 (𝐴 ∪ V) ⊆ V
2 ssun2 4134 . 2 V ⊆ (𝐴 ∪ V)
31, 2eqssi 3961 1 (𝐴 ∪ V) = V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  Vcvv 3444  cun 3909
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-un 3916  df-in 3918  df-ss 3928
This theorem is referenced by:  oev2  8470
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