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Metamath Proof Explorer

Theorem ffdmd

Description: The domain of a function. (Contributed by Glauco Siliprandi, 26-Jun-2021)

		Ref	Expression
	Hypothesis	ffdmd.1	$⊢ φ \to F : A ⟶ B$
	Assertion	ffdmd	$⊢ φ \to F : dom F ⟶ B$

Step	Hyp	Ref	Expression
1		ffdmd.1	$⊢ φ \to F : A ⟶ B$
2		ffdm	$⊢ F : A ⟶ B \to (F : dom F ⟶ B \land dom F \subseteq A)$
3	1 2	syl	$⊢ φ \to (F : dom F ⟶ B \land dom F \subseteq A)$
4	3	simpld	$⊢ φ \to F : dom F ⟶ B$