Theorem unv 4327

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 4108	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3931	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1547  Vcvv 3431   ∪ cun 3881

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-v 3433  df-un 3888  df-ss 3900

This theorem is referenced by:  oev2  8448  dmxrnuncnvepres  38759