Metamath Proof Explorer


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 = ∅