Theorem funmpt2

Description: Functionality of a class given by a maps-to notation. (Contributed by FL, 17-Feb-2008) (Revised by Mario Carneiro, 31-May-2014)

	Ref	Expression
Hypothesis	funmpt2.1	$$⊢F=\left(x\in A⟼B\right)$$
Assertion	funmpt2	$$⊢\mathrm{Fun}F$$

Proof

Step	Hyp	Ref	Expression
1		funmpt2.1	$$⊢F=\left(x\in A⟼B\right)$$
2		funmpt	$$⊢\mathrm{Fun}\left(x\in A⟼B\right)$$
3	1	funeqi	$$⊢\mathrm{Fun}F\leftrightarrow \mathrm{Fun}\left(x\in A⟼B\right)$$
4	2 3	mpbir	$$⊢\mathrm{Fun}F$$