Theorem unv 4349

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 3959	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4129	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3951	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1541  Vcvv 3436   ∪ cun 3900

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-v 3438  df-un 3907  df-ss 3919

This theorem is referenced by:  oev2  8438