Description: A ring isomorphism is a homomorphism. Compare gimghm . (Contributed by AV, 22-Oct-2019) Remove hypotheses. (Revised by SN, 10-Jan-2025)
Ref | Expression | ||
---|---|---|---|
Assertion | rimrhm | ⊢ ( 𝐹 ∈ ( 𝑅 RingIso 𝑆 ) → 𝐹 ∈ ( 𝑅 RingHom 𝑆 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isrim0 | ⊢ ( 𝐹 ∈ ( 𝑅 RingIso 𝑆 ) ↔ ( 𝐹 ∈ ( 𝑅 RingHom 𝑆 ) ∧ ◡ 𝐹 ∈ ( 𝑆 RingHom 𝑅 ) ) ) | |
2 | 1 | simplbi | ⊢ ( 𝐹 ∈ ( 𝑅 RingIso 𝑆 ) → 𝐹 ∈ ( 𝑅 RingHom 𝑆 ) ) |