Theorem ne0d

Description: Deduction form of ne0i . If a class has elements, then it is nonempty. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypothesis	ne0d.1	⊢ ( 𝜑 → 𝐵 ∈ 𝐴 )
Assertion	ne0d	⊢ ( 𝜑 → 𝐴 ≠ ∅ )

Proof

Step	Hyp	Ref	Expression
1		ne0d.1	⊢ ( 𝜑 → 𝐵 ∈ 𝐴 )
2		ne0i	⊢ ( 𝐵 ∈ 𝐴 → 𝐴 ≠ ∅ )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ≠ ∅ )