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Metamath Proof Explorer

Theorem mbf0

Description: The empty function is measurable. (Contributed by Brendan Leahy, 28-Mar-2018)

		Ref	Expression
	Assertion	mbf0	$⊢ \emptyset \in MblFn$

Step	Hyp	Ref	Expression
1		0xp	$⊢ \emptyset \times \{1\} = \emptyset$
2		0mbl	$⊢ \emptyset \in dom vol$
3		ax-1cn	$⊢ 1 \in ℂ$
4		mbfconst	$⊢ (\emptyset \in dom vol \land 1 \in ℂ) \to \emptyset \times \{1\} \in MblFn$
5	2 3 4	mp2an	$⊢ \emptyset \times \{1\} \in MblFn$
6	1 5	eqeltrri	$⊢ \emptyset \in MblFn$