Theorem dffun6

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

	Ref	Expression
Assertion	dffun6	⊢ ( Fun 𝐹 ↔ ( Rel 𝐹 ∧ ∀ 𝑥 ∃* 𝑦 𝑥 𝐹 𝑦 ) )

Proof

Step	Hyp	Ref	Expression
1		nfcv	⊢ Ⅎ 𝑥 𝐹
2		nfcv	⊢ Ⅎ 𝑦 𝐹
3	1 2	dffun6f	⊢ ( Fun 𝐹 ↔ ( Rel 𝐹 ∧ ∀ 𝑥 ∃* 𝑦 𝑥 𝐹 𝑦 ) )