Description: The relation "is isomorphic to" for groups. (Contributed by Stefan O'Rear, 25-Jan-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | brgic | ⊢ ( 𝑅 ≃𝑔 𝑆 ↔ ( 𝑅 GrpIso 𝑆 ) ≠ ∅ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-gic | ⊢ ≃𝑔 = ( ◡ GrpIso “ ( V ∖ 1o ) ) | |
2 | gimfn | ⊢ GrpIso Fn ( Grp × Grp ) | |
3 | 1 2 | brwitnlem | ⊢ ( 𝑅 ≃𝑔 𝑆 ↔ ( 𝑅 GrpIso 𝑆 ) ≠ ∅ ) |