Theorem unv

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)

	Ref	Expression
Assertion	unv	⊢ ( 𝐴 ∪ V ) = V

Proof

Step	Hyp	Ref	Expression
1		ssv	⊢ ( 𝐴 ∪ V ) ⊆ V
2		ssun2	⊢ V ⊆ ( 𝐴 ∪ V )
3	1 2	eqssi	⊢ ( 𝐴 ∪ V ) = V