Metamath Proof Explorer

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 
|- ( ph -> B e. A )
Assertion ne0d 
|- ( ph -> A =/= (/) )

Proof

Step Hyp Ref Expression
1 ne0d.1 
 |-  ( ph -> B e. A )
2 ne0i 
 |-  ( B e. A -> A =/= (/) )
3 1 2 syl 
 |-  ( ph -> A =/= (/) )