Theorem unv 4362

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 3969	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4140	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3961	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1567  Vcvv 3463   ∪ cun 3911

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-v 3465  df-un 3918  df-ss 3930

This theorem is referenced by:  oev2  8504  dmxrnuncnvepres  38926