Theorem n0i

Description: If a class has elements, then it is not empty. (Contributed by NM, 31-Dec-1993)

	Ref	Expression
Assertion	n0i	⊢ ( 𝐵 ∈ 𝐴 → ¬ 𝐴 = ∅ )

Proof

Step	Hyp	Ref	Expression
1		noel	⊢ ¬ 𝐵 ∈ ∅
2		eleq2	⊢ ( 𝐴 = ∅ → ( 𝐵 ∈ 𝐴 ↔ 𝐵 ∈ ∅ ) )
3	1 2	mtbiri	⊢ ( 𝐴 = ∅ → ¬ 𝐵 ∈ 𝐴 )
4	3	con2i	⊢ ( 𝐵 ∈ 𝐴 → ¬ 𝐴 = ∅ )