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Metamath Proof Explorer

Theorem snnz

Description: The singleton of a set is not empty. (Contributed by NM, 10-Apr-1994)

Ref Expression
Hypothesis snnz.1 ⊢ 𝐴 ∈ V
Assertion snnz { 𝐴 } ≠ ∅

Proof

Step Hyp Ref Expression
1 snnz.1 ⊢ 𝐴 ∈ V
2 snnzg ⊢ ( 𝐴 ∈ V → { 𝐴 } ≠ ∅ )
3 1 2 ax-mp ⊢ { 𝐴 } ≠ ∅