Theorem 0nelrel

Description: A binary relation does not contain the empty set. (Contributed by AV, 15-Nov-2021)

	Ref	Expression
Assertion	0nelrel	⊢ ( Rel 𝑅 → ∅ ∉ 𝑅 )

Proof

Step	Hyp	Ref	Expression
1		0nelrel0	⊢ ( Rel 𝑅 → ¬ ∅ ∈ 𝑅 )
2		df-nel	⊢ ( ∅ ∉ 𝑅 ↔ ¬ ∅ ∈ 𝑅 )
3	1 2	sylibr	⊢ ( Rel 𝑅 → ∅ ∉ 𝑅 )