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Metamath Proof Explorer

Theorem regtop

Description: A regular space is a topological space. (Contributed by Jeff Hankins, 1-Feb-2010)

Ref Expression
Assertion regtop 
|- ( J e. Reg -> J e. Top )

Proof

Step Hyp Ref Expression
1 isreg 
 |-  ( J e. Reg <-> ( J e. Top /\ A. x e. J A. y e. x E. z e. J ( y e. z /\ ( ( cls ` J ) ` z ) C_ x ) ) )
2 1 simplbi 
 |-  ( J e. Reg -> J e. Top )