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Metamath Proof Explorer

Theorem unisn0

Description: The union of the singleton of the empty set is the empty set. (Contributed by Glauco Siliprandi, 17-Aug-2020)

		Ref	Expression
	Assertion	unisn0	$⊢ ⋃ \{\emptyset\} = \emptyset$

Step	Hyp	Ref	Expression
1		ssid	$⊢ \{\emptyset\} \subseteq \{\emptyset\}$
2		uni0b	$⊢ ⋃ \{\emptyset\} = \emptyset \leftrightarrow \{\emptyset\} \subseteq \{\emptyset\}$
3	1 2	mpbir	$⊢ ⋃ \{\emptyset\} = \emptyset$