Metamath Proof Explorer

Theorem t1hmph

Description: T_1 is a topological property. (Contributed by Mario Carneiro, 25-Aug-2015)

Ref Expression
Assertion t1hmph 
|- ( J ~= K -> ( J e. Fre -> K e. Fre ) )

Proof

Step Hyp Ref Expression
1 t1top 
 |-  ( J e. Fre -> J e. Top )
2 cnt1 
 |-  ( ( J e. Fre /\ f : U. K -1-1-> U. J /\ f e. ( K Cn J ) ) -> K e. Fre )
3 1 2 haushmphlem 
 |-  ( J ~= K -> ( J e. Fre -> K e. Fre ) )