Theorem unv 4197

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 3851	. 2 ⊢ (𝐴 ∪ V) ⊆ V
2		ssun2 4005	. 2 ⊢ V ⊆ (𝐴 ∪ V)
3	1, 2	eqssi 3844	1 ⊢ (𝐴 ∪ V) = V

Syntax hints:   = wceq 1658  Vcvv 3415   ∪ cun 3797

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-ext 2804

This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2813  df-cleq 2819  df-clel 2822  df-nfc 2959  df-v 3417  df-un 3804  df-in 3806  df-ss 3813

This theorem is referenced by:  oev2  7871