Metamath Proof Explorer


Theorem risci

Description: Determine that two rings are isomorphic. (Contributed by Jeff Madsen, 16-Jun-2011)

Ref Expression
Assertion risci Could not format assertion : No typesetting found for |- ( ( R e. RingOps /\ S e. RingOps /\ F e. ( R RingOpsIso S ) ) -> R ~=R S ) with typecode |-

Proof

Step Hyp Ref Expression
1 elex2 Could not format ( F e. ( R RingOpsIso S ) -> E. f f e. ( R RingOpsIso S ) ) : No typesetting found for |- ( F e. ( R RingOpsIso S ) -> E. f f e. ( R RingOpsIso S ) ) with typecode |-
2 risc Could not format ( ( R e. RingOps /\ S e. RingOps ) -> ( R ~=R S <-> E. f f e. ( R RingOpsIso S ) ) ) : No typesetting found for |- ( ( R e. RingOps /\ S e. RingOps ) -> ( R ~=R S <-> E. f f e. ( R RingOpsIso S ) ) ) with typecode |-
3 1 2 imbitrrid Could not format ( ( R e. RingOps /\ S e. RingOps ) -> ( F e. ( R RingOpsIso S ) -> R ~=R S ) ) : No typesetting found for |- ( ( R e. RingOps /\ S e. RingOps ) -> ( F e. ( R RingOpsIso S ) -> R ~=R S ) ) with typecode |-
4 3 3impia Could not format ( ( R e. RingOps /\ S e. RingOps /\ F e. ( R RingOpsIso S ) ) -> R ~=R S ) : No typesetting found for |- ( ( R e. RingOps /\ S e. RingOps /\ F e. ( R RingOpsIso S ) ) -> R ~=R S ) with typecode |-