Metamath Proof Explorer


Theorem cvmtop1

Description: Reverse closure for a covering map. (Contributed by Mario Carneiro, 11-Feb-2015)

Ref Expression
Assertion cvmtop1 F C CovMap J C Top

Proof

Step Hyp Ref Expression
1 n0i F C CovMap J ¬ C CovMap J =
2 fncvm CovMap Fn Top × Top
3 2 fndmi dom CovMap = Top × Top
4 3 ndmov ¬ C Top J Top C CovMap J =
5 1 4 nsyl2 F C CovMap J C Top J Top
6 5 simpld F C CovMap J C Top