Metamath Proof Explorer

Theorem suc0

Description: The successor of the empty set. (Contributed by NM, 1-Feb-2005)

Ref Expression
Assertion suc0 
|- suc (/) = { (/) }

Proof

Step Hyp Ref Expression
1 df-suc 
 |-  suc (/) = ( (/) u. { (/) } )
2 uncom 
 |-  ( (/) u. { (/) } ) = ( { (/) } u. (/) )
3 un0 
 |-  ( { (/) } u. (/) ) = { (/) }
4 1 2 3 3eqtri 
 |-  suc (/) = { (/) }