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Theorem unv 4079
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 3731 . 2 (𝐴 ∪ V) ⊆ V
2 ssun2 3885 . 2 V ⊆ (𝐴 ∪ V)
31, 2eqssi 3725 1 (𝐴 ∪ V) = V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1596  Vcvv 3304  cun 3678
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-10 2132  ax-11 2147  ax-12 2160  ax-13 2355  ax-ext 2704
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1599  df-ex 1818  df-nf 1823  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-nfc 2855  df-v 3306  df-un 3685  df-in 3687  df-ss 3694
This theorem is referenced by:  oev2  7723
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