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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 noel ⊢ ¬ B ∈ ∅
2 eleq2 ⊢ A = ∅ → B ∈ A ↔ B ∈ ∅
3 1 2 mtbiri ⊢ A = ∅ → ¬ B ∈ A
4 3 con2i ⊢ B ∈ A → ¬ A = ∅