Theorem fdmd

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

	Ref	Expression
Hypothesis	fdmd.1	$$⊢\phi \to F:A⟶B$$
Assertion	fdmd	$$⊢\phi \to \mathrm{dom}F=A$$

Proof

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