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Metamath Proof Explorer

Theorem frexr

Description: A function taking real values, is a function taking extended real values. (Contributed by Glauco Siliprandi, 26-Jun-2021)

		Ref	Expression
	Hypothesis	frexr.1	$⊢ φ \to F : A ⟶ ℝ$
	Assertion	frexr	$⊢ φ \to F : A ⟶ ℝ^{*}$

Step	Hyp	Ref	Expression
1		frexr.1	$⊢ φ \to F : A ⟶ ℝ$
2		ressxr	$⊢ ℝ \subseteq ℝ^{*}$
3	2	a1i	$⊢ φ \to ℝ \subseteq ℝ^{*}$
4	1 3	fssd	$⊢ φ \to F : A ⟶ ℝ^{*}$