Description: Equality inference for function predicate with domain. (Contributed by NM, 4-Sep-2011)
Ref | Expression | ||
---|---|---|---|
Hypothesis | fneq2i.1 | ⊢ 𝐴 = 𝐵 | |
Assertion | fneq2i | ⊢ ( 𝐹 Fn 𝐴 ↔ 𝐹 Fn 𝐵 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fneq2i.1 | ⊢ 𝐴 = 𝐵 | |
2 | fneq2 | ⊢ ( 𝐴 = 𝐵 → ( 𝐹 Fn 𝐴 ↔ 𝐹 Fn 𝐵 ) ) | |
3 | 1 2 | ax-mp | ⊢ ( 𝐹 Fn 𝐴 ↔ 𝐹 Fn 𝐵 ) |