Metamath Proof Explorer

Theorem brgici

Description: Prove isomorphic by an explicit isomorphism. (Contributed by Stefan O'Rear, 25-Jan-2015)

Ref Expression
Assertion brgici 
|- ( F e. ( R GrpIso S ) -> R ~=g S )

Proof

Step Hyp Ref Expression
1 ne0i 
 |-  ( F e. ( R GrpIso S ) -> ( R GrpIso S ) =/= (/) )
2 brgic 
 |-  ( R ~=g S <-> ( R GrpIso S ) =/= (/) )
3 1 2 sylibr 
 |-  ( F e. ( R GrpIso S ) -> R ~=g S )