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 → 𝐹 : 𝐴 ⟶ 𝐵 )
Assertion	fdmd	⊢ ( 𝜑 → dom 𝐹 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		fdmd.1	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
2		fdm	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → dom 𝐹 = 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → dom 𝐹 = 𝐴 )