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Metamath Proof Explorer

Theorem nel02

Description: The empty set has no elements. (Contributed by Peter Mazsa, 4-Jan-2018)

Ref Expression
Assertion nel02 ⊢ A = ∅ → ¬ B ∈ A

Proof

Step Hyp Ref Expression
1 noel ⊢ ¬ B ∈ ∅
2 eleq2 ⊢ A = ∅ → B ∈ A ↔ B ∈ ∅
3 1 2 mtbiri ⊢ A = ∅ → ¬ B ∈ A