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Metamath Proof Explorer

Theorem fdmd

Description: Deduction form of fdm . The domain of a mapping. (Contributed by Glauco Siliprandi, 26-Jun-2021)

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

Step	Hyp	Ref	Expression
1		fdmd.1	$⊢ φ \to F : A ⟶ B$
2		fdm	$⊢ F : A ⟶ B \to dom F = A$
3	1 2	syl	$⊢ φ \to dom F = A$