Theorem unv 4352

Description: The union of a class with the universal class is the universal class. Dual of in0 4348. 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 3937	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4180	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3929	1 ⊢ (𝐴 ∪ V) = V

This proof depends on syntax axioms:   = wceq 1570  Vcvv 3454   ∪ cun 4152

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-un 4154

This theorem is used by:  oev2  8569  dmxrnuncnvepres  39590