This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem 0nelfun

Description: A function does not contain the empty set. (Contributed by BJ, 26-Nov-2021)

		Ref	Expression
	Assertion	0nelfun	⊢ ( Fun 𝑅 → ∅ ∉ 𝑅 )

Step	Hyp	Ref	Expression
1		funrel	⊢ ( Fun 𝑅 → Rel 𝑅 )
2		0nelrel	⊢ ( Rel 𝑅 → ∅ ∉ 𝑅 )
3	1 2	syl	⊢ ( Fun 𝑅 → ∅ ∉ 𝑅 )