Theorem n0ii

Description: If a class has elements, then it is not empty. Inference associated with n0i . (Contributed by BJ, 15-Jul-2021)

	Ref	Expression
Hypothesis	n0ii.1	⊢ 𝐴 ∈ 𝐵
Assertion	n0ii	⊢ ¬ 𝐵 = ∅

Proof

Step	Hyp	Ref	Expression
1		n0ii.1	⊢ 𝐴 ∈ 𝐵
2		n0i	⊢ ( 𝐴 ∈ 𝐵 → ¬ 𝐵 = ∅ )
3	1 2	ax-mp	⊢ ¬ 𝐵 = ∅