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	$$⊢\phi \to B\in A$$
Assertion	ne0d	$$⊢\phi \to A\ne \varnothing$$

Proof

Step	Hyp	Ref	Expression
1		ne0d.1	$$⊢\phi \to B\in A$$
2		ne0i	$$⊢B\in A\to A\ne \varnothing$$
3	1 2	syl	$$⊢\phi \to A\ne \varnothing$$