Theorem unv 4391

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 4002	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4169	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3994	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1534  Vcvv 3469   ∪ cun 3942

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2698

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2705  df-cleq 2719  df-clel 2805  df-v 3471  df-un 3949  df-in 3951  df-ss 3961

This theorem is referenced by:  oev2  8537