Theorem i1fmbf

Description: Simple functions are measurable. (Contributed by Mario Carneiro, 18-Jun-2014)

	Ref	Expression
Assertion	i1fmbf	⊢ ( 𝐹 ∈ dom ∫1 → 𝐹 ∈ MblFn )

Proof

Step	Hyp	Ref	Expression
1		isi1f	⊢ ( 𝐹 ∈ dom ∫1 ↔ ( 𝐹 ∈ MblFn ∧ ( 𝐹 : ℝ ⟶ ℝ ∧ ran 𝐹 ∈ Fin ∧ ( vol ‘ ( ◡ 𝐹 “ ( ℝ ∖ { 0 } ) ) ) ∈ ℝ ) ) )
2	1	simplbi	⊢ ( 𝐹 ∈ dom ∫1 → 𝐹 ∈ MblFn )