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Metamath Proof Explorer

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 nel02 ⊢ ( 𝐴 = ∅ → ¬ 𝐵 ∈ 𝐴 )
2 1 con2i ⊢ ( 𝐵 ∈ 𝐴 → ¬ 𝐴 = ∅ )