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Theorem unv 3917
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 3582 . 2 (𝐴 ∪ V) ⊆ V
2 ssun2 3733 . 2 V ⊆ (𝐴 ∪ V)
31, 2eqssi 3578 1 (𝐴 ∪ V) = V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  Vcvv 3167  cun 3532
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-10 2004  ax-11 2019  ax-12 2031  ax-13 2227  ax-ext 2584
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1866  df-clab 2591  df-cleq 2597  df-clel 2600  df-nfc 2734  df-v 3169  df-un 3539  df-in 3541  df-ss 3548
This theorem is referenced by:  oev2  7462
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