Theorem snn0d

Description: The singleton of a set is not empty. (Contributed by Glauco Siliprandi, 3-Mar-2021)

	Ref	Expression
Hypothesis	snn0d.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
Assertion	snn0d	⊢ ( 𝜑 → { 𝐴 } ≠ ∅ )

Proof

Step	Hyp	Ref	Expression
1		snn0d.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
2		snnzg	⊢ ( 𝐴 ∈ 𝑉 → { 𝐴 } ≠ ∅ )
3	1 2	syl	⊢ ( 𝜑 → { 𝐴 } ≠ ∅ )