Theorem unv 4387

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 3998	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4165	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3990	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1533  Vcvv 3466   ∪ cun 3938

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-un 3945  df-in 3947  df-ss 3957

This theorem is referenced by:  oev2  8518