Theorem unv 4348

Description: The union of a class with the universal class is the universal class. Dual of in0 4344. 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 3932	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4177	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3924	1 ⊢ (𝐴 ∪ V) = V

This proof depends on syntax axioms:   = wceq 1569  Vcvv 3450   ∪ cun 4149

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-un 4151

This theorem is used by:  oev2  8535  dmxrnuncnvepres  39418