Description: Prove isomorphic by an explicit isomorphism. (Contributed by Stefan O'Rear, 25-Jan-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | brgici | ⊢ ( 𝐹 ∈ ( 𝑅 GrpIso 𝑆 ) → 𝑅 ≃𝑔 𝑆 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ne0i | ⊢ ( 𝐹 ∈ ( 𝑅 GrpIso 𝑆 ) → ( 𝑅 GrpIso 𝑆 ) ≠ ∅ ) | |
2 | brgic | ⊢ ( 𝑅 ≃𝑔 𝑆 ↔ ( 𝑅 GrpIso 𝑆 ) ≠ ∅ ) | |
3 | 1 2 | sylibr | ⊢ ( 𝐹 ∈ ( 𝑅 GrpIso 𝑆 ) → 𝑅 ≃𝑔 𝑆 ) |