Theorem fndmd

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

	Ref	Expression
Hypothesis	fndmd.1	⊢ ( 𝜑 → 𝐹 Fn 𝐴 )
Assertion	fndmd	⊢ ( 𝜑 → dom 𝐹 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		fndmd.1	⊢ ( 𝜑 → 𝐹 Fn 𝐴 )
2		fndm	⊢ ( 𝐹 Fn 𝐴 → dom 𝐹 = 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → dom 𝐹 = 𝐴 )