Theorem unv 4394

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 4005	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4172	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3997	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1541  Vcvv 3474   ∪ cun 3945

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-un 3952  df-in 3954  df-ss 3964

This theorem is referenced by:  oev2  8519