Theorem mbf0

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

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

Proof

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