Theorem unv 4350

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 3958	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4129	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3950	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1559  Vcvv 3453   ∪ cun 3900

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1562  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3455  df-un 3907  df-ss 3919

This theorem is referenced by:  oev2  8486  dmxrnuncnvepres  38852