Metamath Proof Explorer

Theorem t0hmph

Description: T_0 is a topological property. (Contributed by Mario Carneiro, 25-Aug-2015)

Ref Expression
Assertion t0hmph 
|- ( J ~= K -> ( J e. Kol2 -> K e. Kol2 ) )

Proof

Step Hyp Ref Expression
1 t0top 
 |-  ( J e. Kol2 -> J e. Top )
2 cnt0 
 |-  ( ( J e. Kol2 /\ f : U. K -1-1-> U. J /\ f e. ( K Cn J ) ) -> K e. Kol2 )
3 1 2 haushmphlem 
 |-  ( J ~= K -> ( J e. Kol2 -> K e. Kol2 ) )