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Metamath Proof Explorer

Theorem fndmd

Description: The domain of a function. (Contributed by Glauco Siliprandi, 23-Oct-2021)

		Ref	Expression
	Hypothesis	fndmd.1	$⊢ φ \to F Fn A$
	Assertion	fndmd	$⊢ φ \to dom F = A$

Step	Hyp	Ref	Expression
1		fndmd.1	$⊢ φ \to F Fn A$
2		fndm	$⊢ F Fn A \to dom F = A$
3	1 2	syl	$⊢ φ \to dom F = A$