Metamath Proof Explorer

Theorem 0sald

Description: The empty set belongs to every sigma-algebra. (Contributed by Glauco Siliprandi, 26-Jun-2021)

Ref Expression
Hypothesis 0sald.1 
|- ( ph -> S e. SAlg )
Assertion 0sald 
|- ( ph -> (/) e. S )

Proof

Step Hyp Ref Expression
1 0sald.1 
 |-  ( ph -> S e. SAlg )
2 0sal 
 |-  ( S e. SAlg -> (/) e. S )
3 1 2 syl 
 |-  ( ph -> (/) e. S )