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Metamath Proof Explorer

Theorem ne0i

Description: If a class has elements, then it is nonempty. (Contributed by NM, 31-Dec-1993)

Ref Expression
Assertion ne0i ( 𝐵 ∈ 𝐴 → 𝐴 ≠ ∅ )

Proof

Step Hyp Ref Expression
1 n0i ⊢ ( 𝐵 ∈ 𝐴 → ¬ 𝐴 = ∅ )
2 1 neqned ⊢ ( 𝐵 ∈ 𝐴 → 𝐴 ≠ ∅ )