Theorem unv 4326

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 3941	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4103	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3933	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1539  Vcvv 3422   ∪ cun 3881

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-un 3888  df-in 3890  df-ss 3900

This theorem is referenced by:  oev2  8315