Metamath Proof Explorer

Theorem ttcsnssg

Description: The transitive closure is contained in the singleton transitive closure. (Contributed by Matthew House, 6-Apr-2026)

Ref Expression
Assertion ttcsnssg 
|- ( A e. V -> TC+ A C_ TC+ { A } )

Proof

Step Hyp Ref Expression
1 snidg 
 |-  ( A e. V -> A e. { A } )
2 ttcel2 
 |-  ( A e. { A } -> TC+ A C_ TC+ { A } )
3 1 2 syl 
 |-  ( A e. V -> TC+ A C_ TC+ { A } )