Theorem dffun6

Description: Alternate definition of a function using "at most one" notation. (Contributed by NM, 9-Mar-1995)

	Ref	Expression
Assertion	dffun6	$$⊢\mathrm{Fun}F\leftrightarrow \left(\mathrm{Rel}F\wedge \forall x{\exists }^{*}yxFy\right)$$

Proof

Step	Hyp	Ref	Expression
1		nfcv	$$⊢\underset{\_}{Ⅎ}xF$$
2		nfcv	$$⊢\underset{\_}{Ⅎ}yF$$
3	1 2	dffun6f	$$⊢\mathrm{Fun}F\leftrightarrow \left(\mathrm{Rel}F\wedge \forall x{\exists }^{*}yxFy\right)$$