Metamath Proof Explorer

Theorem unisn0

Description: The union of the singleton of the empty set is the empty set. (Contributed by Glauco Siliprandi, 17-Aug-2020)

Ref Expression
Assertion unisn0 
|- U. { (/) } = (/)

Proof

Step Hyp Ref Expression
1 ssid 
 |-  { (/) } C_ { (/) }
2 uni0b 
 |-  ( U. { (/) } = (/) <-> { (/) } C_ { (/) } )
3 1 2 mpbir 
 |-  U. { (/) } = (/)