Theorem unv 4353

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

Step	Hyp	Ref	Expression
1		ssv 3960	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4133	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3952	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1542  Vcvv 3442   ∪ cun 3901

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 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3444  df-un 3908  df-ss 3920

This theorem is referenced by:  oev2  8460  dmxrnuncnvepres  38640