Theorem unv 4356

Description: The union of a class with the universal class is the universal class. Dual of in0 4352. 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 4132	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3954	1 ⊢ (𝐴 ∪ V) = V

This proof depends on syntax axioms:   = wceq 1570  Vcvv 3457   ∪ cun 3904

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-un 3911  df-ss 3923

This theorem is used by:  oev2  8510  dmxrnuncnvepres  39074