Theorem unv 4303

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 3939	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4100	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3931	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1538  Vcvv 3441   ∪ cun 3879

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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-un 3886  df-in 3888  df-ss 3898

This theorem is referenced by:  oev2  8131