Theorem dmmpti

Description: Domain of the mapping operation. (Contributed by NM, 6-Sep-2005) (Revised by Mario Carneiro, 31-Aug-2015)

	Ref	Expression
Hypotheses	fnmpti.1	$$⊢B\in \mathrm{V}$$
	fnmpti.2	$$⊢F=\left(x\in A⟼B\right)$$
Assertion	dmmpti	$$⊢\mathrm{dom}F=A$$

Proof

Step	Hyp	Ref	Expression
1		fnmpti.1	$$⊢B\in \mathrm{V}$$
2		fnmpti.2	$$⊢F=\left(x\in A⟼B\right)$$
3	1 2	fnmpti	$$⊢FFnA$$
4	3	fndmi	$$⊢\mathrm{dom}F=A$$