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Metamath Proof Explorer

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	$⊢ A \cup V = V$

Proof

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