Metamath Proof Explorer


Theorem isrisc

Description: The ring isomorphism relation. (Contributed by Jeff Madsen, 16-Jun-2011)

Ref Expression
Hypotheses isrisc.1 RV
isrisc.2 SV
Assertion isrisc Could not format assertion : No typesetting found for |- ( R ~=R S <-> ( ( R e. RingOps /\ S e. RingOps ) /\ E. f f e. ( R RingOpsIso S ) ) ) with typecode |-

Proof

Step Hyp Ref Expression
1 isrisc.1 RV
2 isrisc.2 SV
3 isriscg Could not format ( ( R e. _V /\ S e. _V ) -> ( R ~=R S <-> ( ( R e. RingOps /\ S e. RingOps ) /\ E. f f e. ( R RingOpsIso S ) ) ) ) : No typesetting found for |- ( ( R e. _V /\ S e. _V ) -> ( R ~=R S <-> ( ( R e. RingOps /\ S e. RingOps ) /\ E. f f e. ( R RingOpsIso S ) ) ) ) with typecode |-
4 1 2 3 mp2an Could not format ( R ~=R S <-> ( ( R e. RingOps /\ S e. RingOps ) /\ E. f f e. ( R RingOpsIso S ) ) ) : No typesetting found for |- ( R ~=R S <-> ( ( R e. RingOps /\ S e. RingOps ) /\ E. f f e. ( R RingOpsIso S ) ) ) with typecode |-