Theorem unv 4357

Description: The union of a class with the universal class is the universal class. Dual of in0 4353. 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 3962	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4133	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3954	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1570  Vcvv 3455   ∪ cun 3904

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457  df-un 3911  df-ss 3923

This theorem is referenced by:  oev2  8509  dmxrnuncnvepres  39022