Theorem unv

Description: The union of a class with the universal class is the universal class. Dual of in0 . Exercise 4.10(l) of Mendelson p. 231. (Contributed by NM, 17-May-1998)

	Ref	Expression
Assertion	unv	$$⊢A\cup \mathrm{V}=\mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		ssv	$$⊢A\cup \mathrm{V}\subseteq \mathrm{V}$$
2		ssun2	$$⊢\mathrm{V}\subseteq A\cup \mathrm{V}$$
3	1 2	eqssi	$$⊢A\cup \mathrm{V}=\mathrm{V}$$