Theorem nel02

Description: The empty set has no elements. (Contributed by Peter Mazsa, 4-Jan-2018)

	Ref	Expression
Assertion	nel02	⊢ ( 𝐴 = ∅ → ¬ 𝐵 ∈ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		noel	⊢ ¬ 𝐵 ∈ ∅
2		eleq2	⊢ ( 𝐴 = ∅ → ( 𝐵 ∈ 𝐴 ↔ 𝐵 ∈ ∅ ) )
3	1 2	mtbiri	⊢ ( 𝐴 = ∅ → ¬ 𝐵 ∈ 𝐴 )