Theorem unv 4405

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 4020	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4189	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 4012	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1537  Vcvv 3478   ∪ cun 3961

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-un 3968  df-ss 3980

This theorem is referenced by:  oev2  8560