Theorem nrmreg

Description: A normal T_1 space is regular Hausdorff. In other words, a T_4 space is T_3 . One can get away with slightly weaker assumptions; see nrmr0reg . (Contributed by Mario Carneiro, 25-Aug-2015)

	Ref	Expression
Assertion	nrmreg	|- ( ( J e. Nrm /\ J e. Fre ) -> J e. Reg )

Proof

Step	Hyp	Ref	Expression
1		t1r0	|- ( J e. Fre -> ( KQ ` J ) e. Fre )
2		nrmr0reg	|- ( ( J e. Nrm /\ ( KQ ` J ) e. Fre ) -> J e. Reg )
3	1 2	sylan2	|- ( ( J e. Nrm /\ J e. Fre ) -> J e. Reg )