Theorem unv 4374

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 3983	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4154	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3975	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1540  Vcvv 3459   ∪ cun 3924

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-v 3461  df-un 3931  df-ss 3943

This theorem is referenced by:  oev2  8533